Related papers: On the freezing of variables in random constraint …
We propose a simple dynamical model of the glass transition based on the results from a non-randomly frustrated spin model which is known to form a glassy state below a characteristic quench temperature. The model is characterized by a…
The gauge theory of spin glasses and statistical-mechanical formulation of error-correcting codes are reviewed with an emphasis on their similarities. For the gauge theory, we explain the functional identities on dynamical autocorrelation…
This paper studies a Large Language Model's ability to exhibit intelligence equivalent to that of a human by analyzing temperature-induced phase transitions, abrupt changes in the macroscopic behavior of a system, in the Turing test. We…
Soft-granular media, such as dense emulsions, foams or tissues, exhibit either fluid- or solid-like properties depending on the applied external stresses. Whereas bulk rheology of such materials has been thoroughly investigated, the…
A feedback vertex set (FVS) of an undirected graph contains vertices from every cycle of this graph. Constructing a FVS of sufficiently small cardinality is very difficult in the worst cases, but for random graphs this problem can be…
We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light…
We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to…
Glass transition where viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics (Cavagna, 2009;…
We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis…
We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (magnetic field). Previous studies at zero field have shown a remarkable equilibrium…
A systematic investigation is presented of grain boundaries and grain boundary networks in two dimensional flexible membranes with crystalline order. An isolated grain boundary undergoes a buckling transition at a critical value of the…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…
In this work it is studied the Hopfield fermionic spin glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
We prove that the Aizenman-Contucci relations, well known for fully connected spin glasses, hold in diluted spin glasses as well. We also prove more general constraints in the same spirit for multi-overlaps, systematically confirming and…
We study the problem of predictability, or "nature vs. nurture", in several disordered Ising spin systems evolving at zero temperature from a random initial state: how much does the final state depend on the information contained in the…
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure…
Quantum kinetically constrained models can exhibit a wealth of dynamical phenomena ranging from anomalous transport to Hilbert-space fragmentation (HSF). We study a class of one-dimensional particle number conserving systems where particle…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
A particle in a random potential with logarithmic correlations in dimensions $d=1,2$ is shown to undergo a dynamical transition at $T_{dyn}>0$. In $d=1$ exact results demonstrate that $T_{dyn}=T_c$, the static glass transition temperature,…