Statistical Mechanics

We study disordered and frustrated systems such as spin-glasses, structural glasses and random photonics models by means of advanced methods in statistical mechanical of disordered and complex systems, namely Replica Symmetry Breaking theory, Cavity method, Belief and Survey propagation, Supersymmetric path integral formulation of the dynamics (à la Martin-Siggia-Rose), Renormalization group approaches (on hierarchical lattice, on finite dimensional squared and cubic cells, on hierarchical models) and enhanced Monte Carlo methods for the numerical simulation of the dynamics both at and off-equilibrium.


By means of the above mentioned techniques we investigate phase transitions and states organisation in complex systems both at high dimensionality, where the mean-field approximation is exact) and in low dimension, where a phase transition is still present but it belongs to a different universally class. Phenomena studied in the recent years are the spin-glass transition and the low temperature replica symmetry breaking, the structural glass transition and of the organisation of the stable and metastable glassy states below the dynamic arrest transition, the random field Ising model transition, the Anderson localization.


Glassy and slowly relaxing systems. A glass can be viewed as a liquid in which a huge slowing down of the diffusive motion of the particles has destroyed its ability to flow on experimental timescales. The slowing down is expressed through the relaxation time, that is, generally speaking, the characteristic time at which the slowest measurable processes relax to equilibrium. Cooling down from the liquid phase, the slow degrees of freedom of the glass former are no longer accessible and the viscosity of the undercooled melt grows several orders of magnitude in a relatively small temperature interval. As a result, in the cooling process, from some point on, the time effectively spent at a certain temperature is not enough to attain equilibrium: the system is said to have fallen out of equilibrium. Nature and characterization of this non-equilibrium glassy regime and of the glass transition are a challenging issue that stimulates deep theoretical work concerning frustrated systems in diverse representations. We work on the theoretical representation of the behavior of viscous liquids, structural glasses and spin-glasses, on the critical slowing down occurring near-by the dynamic arrest, on the aging dynamics, on the extension of glass theories beyond the limit of validity of mean-field approximation.


Inverse problem in statistical mechanics. Given a data set and a model with some unknown parameters, the inverse problem aims to find the values of the model parameters that best fit the data. We focus on systems of interacting elements, in which the inverse problem concerns the statistical inference of the underling interaction network and of its coupling coefficients from observed data on the dynamics of the system. Versions of this problem are encountered in physics, biology, social sciences and finance, neuroscience (just to cite a few), and are becoming more and more important due to the increase in the amount of data available from these fields. A standard approach used in statistical inference is to predict the interaction couplings by maximizing the likelihood function. This technique, however, requires the evaluation of the partition function that, in the most general case, concerns a number of computations scaling exponentially with the system size. Boltzmann machine learning approach uses Monte Carlo sampling to compute the gradients of the Log-likelihood looking for stationary points but this method is computationally manageable only for small systems. A series of faster approximations, such as naive mean-field, independent-pair approximation inversion of Thouless-Anderson-Palmer equations, small correlations expansion, adaptive TAP, adaptive cluster expansion or Bethe approximations have been developed in the last 15 years. These techniques take as input means and correlations of observed variables and most of them assume a fully connected graph as underlying connectivity network, or expand around it by perturbative dilution. In most cases, network reconstruction turns out to be not accurate for small data sizes and/or when couplings are strong or, else, if the original interaction network is sparse. A further method, substantially improving performances for small data, is the so-called Pseudo-Likelyhood Method (PLM), implemented with regularization or with decimation. We work on the analysis of the performances of the various inference methods, on their improvement and on their application to new problems.


Disordered protein states. The ordered structure of proteins is one of the basic paradigms of classical biology, and it provides an explanation for many aspects of their functioning. Nevertheless, in many cases proteins operate in environments far from equilibrium, or possess labile conformations that convert towards order only under particular conditions. Examples include protein folding/unfolding in the presence of temperature and pressure variations, or configuration reorganizations induced by ligand binding in intrinsically disordered proteins. The statistical properties of these ensembles of structures can be studied with sampling techniques based on classical molecular dynamics simulations.


Molecular networks. We are interested in characterizing emergent properties of large networks of interacting molecules of biological significance, e.g. proteins or nucleic acids, using equilibrium and non-equilibrium statistical mechanics methods. Our central goal is to understand what makes these networks optimal and in which precise sense, how the laws of physics limit their performance in such tasks as noise or information processing, and whether they can sustain collective effects similar to those that characterize more traditional systems studied in statistical physics. In turn, our hope is to gain insight about the evolution of the large-scale organization of the known molecular networks that govern cellular and multi-cellular activities.

Facilities and Labs

“Statistical mechanics and complex photonics” SMCP group



De Martino

CNR Researcher



CNR Researcher



CNR PostDoc



CNR PostDoc



CNR Researcher



Full Professor



CNR PostDoc



CNR Researcher



Full Professor


Ricci Tersenghi

Associate Professor


  1. A. Marruzzo, L Leuzzi, Multi-body quenched disordered XY and p-clock models on random graphs, Physical Review B 93, 094206 (2016) Doi: 10.1103/PhysRevB.93.094206 .
  2. F Antenucci, Statistical Physics of Wave Interactions, Springer (2016)
  3. J. L. Neira, B. Rizzuti, J. L. Iovanna, Determinants of the pKa values of ionizable residues in an intrinsically disordered protein, Archives of Biochemistry and Biophysics, 595, 1-16, (2016) doi: 10.1016/
  4. D De Martino et al, Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli, Phys Biol 13:036005 (2016) DOI: 10.1088/1478-3975/13/3/036005
  5. S Grigolon et al, Noise Processing by MicroRNA-Mediated Circuits: the Incoherent Feed-Forward Loop, Revisited, Heliyon 2:e00095 (2016) DOI: 10.1016/j.heliyon.2016.e00095
  6. Martirosyan et al, Probing the Limits to MicroRNA-Mediated Control of Gene Expression, PLOS Comp Biol 12(1): e1004715 (2016) DOI: 10.1371/journal.pcbi.1004715
  7. C Rainone, U Ferrari, M Paoluzzi, L Leuzzi, Dynamical arrest with zero complexity: The unusual behavior of the spherical Blume-Emery-Griffiths disordered model, Physical Review E 92, 062150 (2015)DOI: 10.1103/PhysRevE.92.062150 .
  8. L Leuzzi, G Parisi, F Ricci-Tersenghi, JJ Ruiz-Lorenzo,Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension, Physical Review B 91, 064202 (2015) DOI: 10.1103/PhysRevB.91.064202.
  9. A Crisanti, L Leuzzi, A simple spin model for three step relaxation and secondary processes in glass formers, Journal of Non-Crystalline Solids 407, 110-117 (2015) DOI: 10.1016/j.jnoncrysol.2014.07.048.
  10. FL Metz, G Parisi,  L Leuzzi, Finite-size corrections to the spectrum of regular random graphs: An analytical solution. Physical Review E 90, 052109 (2014)DOI: 10.1103/PhysRevE.90.052109 .
  11. F Antenucci, A Crisanti, L Leuzzi, Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions,  Physical Review E 90, 012112 (2014) DOI: 10.1103/PhysRevE.90.012112.
  12. F Antenucci, A Crisanti, L Leuzzi, Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models,  Journal of Statistical Physics 155, 909-931 (2014) DOI: 10.1 007/s10955-014-0977-z .
  13. FL Metz, L Leuzzi, G Parisi, Renormalization flow of the hierarchical Anderson model at weak disorder, Physical Review B 89, 064201 (2014) DOI: 10.1103/PhysRevB.89.064201
  14. A Crisanti, L Leuzzi, Large Deviations in Physics, Large Deviations in Disordered Spin Systems,  Springer, 135-160 (2014) .
  15. D De Martino et al. Inferring metabolic phenotypes from the exometabolome through a thermodynamic variational principle. New J Phys 16: 115018 (2014) DOI: 10.1088/1367-2630/16/11/115018
  16. M Figliuzzi et al, RNA based regulation: dynamics and response to perturbations of competing RNAs. Biophys J 107:1011 (2014) Doi: 10.1016/j.bpj.2014.06.035
  17. A De Martino et al, Identifying all moiety conservation laws in genome-scale metabolic networks. PLOS ONE 9:e100750 (2014) Doi: 10.1371/journal.pone.0100750
  18. A Seganti et al. Searching for feasible stationary states in reaction net- works by solving a Boolean constraint satisfaction problem. Phys Rev E 89:022139 (2014) Doi: 10.1103/PhysRevE.89.022139

Other selected publications

  1. B. Rizzuti, V. Daggett, Using simulations to provide the framework for experimental protein folding studies, Archives of Biochemistry and Biophysics 531, 128-135, (2013) doi: 10.1016/
  2. M Figliuzzi et al, MicroRNAs as a selective channel of communication between competing RNAs. Biophys J 104:1203 (2013) DOI: 10.1016/j.bpj.2013.01.012
  3. A Seganti et al. Boolean constraint satisfaction problems for reaction networks. J Stat Mech P09009 (2013) DOI: 10.1088/1742-5468/2013/09/P09009
  4. D De Martino et al. Counting and correcting thermodynamically infeasible flux cycles in genome-scale metabolic networks. Metabolites 3:946 (2013) DOI: 10.3390/metabo3040946
  5. FA Massucci et al. A novel methodology to estimate metabolic flux distributions in constraint-based models. Metabolites 3:838 (2013) DOI: 10.3390/metabo3030838
  6. F Caltagirone, U Ferrari, L Leuzzi, G Parisi, F Ricci-Tersenghi, T Rizzo, Critical Slowing Down Exponents of Mode Coupling Theory, Physical Review Letters, 108, 085702 (2012) DOI: 10.1103/PhysRevLett.108.085702.
  7. L Leuzzi, G Parisi, F Ricci-Tersenghi, JJ Ruiz-Lorenzo, Ising spin-glass transition in a magnetic field outside the limit of validity of mean-field theory, Physical Review Letters 103, 267201 (2009) DOI: 10.1103/PhysRevLett.103.267201.
  8. L Leuzzi, G Parisi, F Ricci-Tersenghi, JJ Ruiz-Lorenzo, Dilute one-dimensional spin glasses with power law decaying interactions,  Physical Review Letters 101, 107203 (2008) DOI: 10.1103/PhysRevLett.101.107203 .
  9. L Leuzzi, TM Nieuwenhuizen, Thermodynamics of the glassy state,  Taylor & Francis, CRC Press (2007)
  10. A Crisanti, L Leuzzi, Stable solution of the simplest spin model for inverse freezing,  Physical Review Letters 95, 087201 (2005) Doi: 10.1103/PhysRevLett.95.087201.


  1. LoTGlaSy: Low Temperature Glassy System, ERC advanced, (2015-2020)
  2. Simons Collaboration on Cracking the Glass Problem: (2015-2020)
  3. Meccanica statistica e complessità, PRIN 2015-2018, (2015-2018)

Latest News

Technology Trasfer in Nanotechnology

Technology Transfer in Nanotechnology: Challenges and Opportunity

Lecce, 18/19 ottobre 2018

CNR NANOTEC c/o Campus Ecotekne

JRC in collaboration with the National Research Council (Cnr) is organising a workshop on Technology Transfer in Nanotechnology,

which will take place in CNR Nanotec (Lecce, Italy) on 18 and 19 October. This workshop is organised in the framework of the TTO-CIRCLE initiatives.   The aim of this event is to explore how technology transfer activities can be used as a mechanism to help EU industry, particularly Start-ups and SMEs, and Government in deploying and adopting Nano-technology. Practical examples will be presented to illustrate the potential of technology transfer in this area.   The workshop will gather technology providers, industry executives, technology transfer officers, policy makers and financial intermediaries to share experiences and lessons learned. One of the key objectives is to discuss policy implications at all levels that could help accelerating the adoption of Nanotechnology by the European manufacturing industry. More informations: Download Locandina

Nanotechnology Transfer Day

26 Luglio 2018 - Lecce

CNR NANOTEC c/o Campus Ecotekne Siglato l’accordo lo scorso maggio tra CNR NANOTEC e Pairstech Capital Management, ha preso il via la collaborazione con PhD TT per la valutazione della ricerca

E’partita la collaborazione con PhD TT per la valorizzazione della ricerca sulla base dell’accordo siglato lo scorso Maggio tra CNR NANOTEC e Pairstech Capital Management, società di gestione patrimoniale che fornisce agli investitori istituzionali e privati un insieme di veicoli di investimento, al fine di valorizzare i risultati della ricerca svolta all'interno dell'Istituto.

Giovedì 19 Luglio dalle ore 11 alle ore 14 nella sede del CNR Nanotec di Lecce si è tenuto un incontro sul trasferimento tecnologico nel settore delle nanotecnologie applicate al settore biomedicale.

L’evento è stato organizzato dall’ufficio di Trasferimento Tecnologico del CNR Nanotec che ha inaugurato con questa giornata un ciclo di eventi mirato a presentare agli attori dell’ecosistema dell’innovazione nel settore delle nanotecnologie i vari modelli e alcune best practice di trasferimento tecnologico. In questa prima giornata il dott. Heber Verri e la dott.ssa Paola Urbani hanno presentato il nuovo modello di trasferimento tecnologico PhD TTãIndex Model.

PhD TT è una realtà italiana completamente indipendente specializzata in trasferimento tecnologico, è un acceleratore organizzato per il Go to Venture Practice, orientata al mondo delle Lifes Sciences.

PhD TT ha sviluppato un nuovo modello di trasferimento tecnologico: il PhD TT©INDEX MODEL dedicato alla generazione di valore dell'innovazione, focalizzato alla riduzione dei rischi delle opportunità di investimento a sostegno della ricerca.

I ricercatori intervengono attivamente nell'analisi iniziale di fattibilità e nella costituzione della futura società (start-up), con l'obiettivo di attrarre capitale di rischio utile a sostenere la fase del trasferimento tecnologico nella visione della "Research for go-to-market".

Il modello PhD TT nasce da un bisogno del mercato, quello di far dialogare due mondi estremamente diversi tra loro: il mondo della ricerca e il mondo degli investimenti.

PhD TT supporta tutte le attività in collaborazione con il TTO - CNR Nanotec con un team di lavoro esperto e grazie a un comitato scientifico-economico qualificato.

In occasione dell'evento del 19/7 u.s. al CNR Nanotec di Lecce, PHD TT ha presentato il proprio track record, dove si sono potuti valutare in dettaglio i casi di successo di intervento del PhD TT©INDEX MODEL.

  Comunicato Stampa Photo Gallery

Disordered serendipity: a glassy path to discovery

A workshop in honour of Giorgio Parisi’s 70th birthday

September 19-21, 2018 - Roma

Sapienza University

With the occasion of celebrating Giorgio Parisi 70th birthday, the conference "Disordered serendipity: a glassy path to discovery" brings to Rome many among the world-leading experts in the field of complex systems. In order to properly represent the many fields of research where Giorgio Parisi gave a relevant contribution in his studies of disordered systems, the conference covers a broad spectrum of topics: from  fundamental and rigorous analysis of the statistical mechanics of disorder systems to applications in biology and computer science. These subjects are deeply interconnected since they are characterized by the presence of glassy behavior.