Related papers: Continuous and discontinuous transitions in genera…
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear…
We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a…
In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the…
The recently proposed strategy for studying the equilibrium thermodynamics of the glass phase using a molecular liquid is reviewed and tested in details on the solvable case of the $p$-spin model. We derive the general phase diagram, and…
The four-dimensional +-J random-bond Ising model is studied using ground-state calculations. System sizes up to N=6^4 spins are considered. Here it is found that the ferromagnetic-spin glass transition occurs at a critical concentration…
Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the…
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field,…
We consider the thermodynamics of an infinite-range Ising p-spin glass model with an additional r-spin ferromagnetic interaction. For r=2 there is a continuous transition to a ferromagnetic phase, while for r>2 the transition is first…
We study a large-$N$ bosonic quantum mechanical sigma-model with a spherical target space subject to disordered interactions, more colloquially known as the $p$-spin spherical model. Replica symmetry is broken at low temperatures and for…
We study the fluctuation problems at high temperature in the general mixed $p$-spin glass models under the weak external field assumption: $h= \rho N^{-\alpha}, \rho>0, \alpha \in [1/4,\infty]$. By extending the cluster expansion approach…
We analyze the infinite range Ising spin-glass in a transverse-field below the critical temperature by a one step replica symmetry theory(1S-RSB). The set of n replicas is divided in r blocks of m replicas each. We present results for…
We study the static as well as the glassy or dynamical transition in the mean-field $p$-state Potts glass. By numerical solution of the saddle point equations we investigate the static and the dynamical transition for all values of $p$ in…
The spherical p-spin model is not only a fundamental model in statistical mechanics of disordered system, but has recently gained popularity since many hard problems in machine learning can be mapped on it. Thus the study of the out of…
The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica…
Dynamic scaling analyses are performed in the spin-glass phase of the $\pm J$ Ising, the {\it XY}, and the Heisenberg models in three dimensions. We found a crossover from the critical dynamics to the ground-state dynamics in the Ising…
We prove the existence of one-step replica symmetry breaking (1RSB) for the mean field Ising spin glasses at finite temperature and identify the first critical temperature in Gardner transition. Specifically, Gardner conjectured that for…
We have studied dynamical behaviour of the infinite-range Ising spin glass model with $p$-spin interaction above and below the transition into the non-ergodic phase. The transition is continuous at sufficiently high external magnetic field.…
We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a.We approximate the influence of the surrounding rods onto dynamics of a pair of…
We show that in the Ising pure $p$-spin model of spin glasses, shattering takes place at all inverse temperatures $\beta \in (\sqrt{(2 \log p)/p}, \sqrt{2\log 2})$ when $p$ is sufficiently large as a function of $\beta$. Of special interest…
We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking Ansatz we can solve exactly the saddle-point equations for…