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The interpolation method is a powerful tool for rigorous analysis of mean-field spin glass models, both with and without dilution. In this study, we show that the interpolation method can be applied to Ising spin glass models in one…
We study the stochastic relaxation dynamics of the Ising p-spin model on a random graph, a well-known model with glassy dynamics at low temperatures. We introduce and discuss a new closure scheme for the master equation governing the…
Complex disordered states - from liquids and glasses to exotic quantum matter - are ubiquitous in nature. Their key properties include finite entropy, power-law correlations and emergent organising principles. In spin ice, spin correlations…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
We derive the exact internal energies and the rigorous upper bounds of specific heats for several spin glass models by applying the gauge theory to the Fortuin-Kasteleyn representation which is a representation based on a percolation…
We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…
Extensive experimental and numerical studies of the non-equilibrium dynamics of spin glasses subjected to temperature or bond perturbations have been performed to investigate chaos and memory effects in selected spin glass systems.…
We study the three-dimensional Kasteleyn transition in both nearest neighbours and dipolar spin ice models using an algorithm that conserves the number of excitations. We first limit the interactions range to nearest neighbours to test the…
After developing an appropriate iteration procedure for the determination of the parameters, the method of simulated tempering has been successfully applied to the 2D Ising spin glass. The reduction of the slowing down is comparable to that…
The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large…
We demonstrate quantum circuit simulations of the transverse field Ising model with longitudinal fields, displaying salient features of glassy dynamics. The energy landscape and spin configurations of toy models are considered, using the…
Antiferromagnetic Ising models on frustrated lattices can realize classical spin liquids, with highly degenerate ground states and, possibly, fractionalized excitations and emergent gauge fields. Motivated by the recent interest in…
A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the…
We consider discrete spin models on arbitrary planar graphs and lattices with frustrated interactions. We first analyze the Ising model with frustrated plaquettes. We use an algebraic approach to derive the result that an Ising model with…
We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility,…
We propose a general method for studying systems that display excitations with arbitrarily low energy in their low-temperature phase. We argue that in a rectangular right prism geometry, with longitudinal size much larger than the…
Using the dedicated computer Janus, we follow the nonequilibrium dynamics of the Ising spin glass in three dimensions for eleven orders of magnitude. The use of integral estimators for the coherence and correlation lengths allows us to…
A bond-disordered two-dimensional Ising model is used to simulate Kauzmann's mechanism of vitrification in liquids, by a Glauber Monte Carlo simulation. The rearrangement of configurations is achieved by allowing impurity bonds to hop to…
Counting the number of ground states for a spin-glass or NP-complete combinatorial optimization problem is even more difficult than the already hard task of finding a single ground state. In this paper the entropy of minimum vertex-covers…
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…