Related papers: Proof of entropic order in Generalized Ising Model…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
The problem of covering the ground set of two matroids by a minimum number of common independent sets is notoriously hard even in very restricted settings, i.e.\ when the goal is to decide if two common independent sets suffice or not.…
Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states $q=3,4$ in $d$…
In glass physics, order parameters have long been used in the thermodynamic description of glasses, but the nature is not yet clear. The difficulty is how to find order in disordered systems. The usual treatment of glass as an exceptional…
We consider lattice implementation of the recently proposed gauge invariant definition of the monopole charge. Because of the lattice discretization the algorithm gives rise to specific lattice artifacts and an effective Ising model. The…
We observe the emergence of a disorder-induced insulating state in a strongly interacting atomic Fermi gas trapped in an optical lattice. This closed quantum system free of a thermal reservoir realizes the disordered Fermi-Hubbard model,…
Random quenched dilution of the triangular-lattice antiferromagnetic Ising model locally relieves frustration, leading to ordering phenomena. We have studied this system, under such dilution of one sublattice, using hard-spin mean-field…
We discuss the microscopic mechanisms by which low-temperature amorphous states, such as ultrastable glasses, transform into equilibrium fluids, after a sudden temperature increase. Experiments suggest that this process is similar to the…
We use computer simulations to probe the thermodynamic and dynamic properties of a glass-former that undergoes an ideal glass-transition because of the presence of randomly pinned particles. We find that even deep in the equilibrium glass…
We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour…
In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field…
The multifractal properties of the Edwards-Anderson order parameter of the short-range Ising spin glass model on d=3 diamond hierarchical lattices is studied via an exact recursion procedure. The profiles of the local order parameter are…
Models of spin glasses are studied with a phase transition discontinuous in the Parisi order parameter. It is assumed that the leading order corrections to the thermodynamic limit of the high temperature free energy are due to the existence…
A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered, like granular media these systems have an extensive entropy of metastable states. We consider the problem of what…
We use an entropy based method to study two graph maximization problems. We upper bound the number of matchings of fixed size $\ell$ in a $d$-regular graph on $N$ vertices. For $\frac{2\ell}{N}$ bounded away from 0 and 1, the logarithm of…
We study the effect of thermal fluctuations in the XY-model on a surface with non vanishing mean curvature and zero Gaussian curvature. Unlike Gaussian curvature that typically frustrates orientational order, the extrinsic curvature of the…
We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander…
We propose a theory based on simple physical arguments that describes a non equilibrium steady-state by a temperature-like parameter (an "effective temperature"). We show how one can predict the effective temperature as a function of the…