Related papers: Replica Cluster Variational Method: the Replica Sy…
We discuss generation of series expansions for Ising spin-glasses with a symmetric $\pm J$ (i.e. bimodal) distribution on d-dimensional hypercubic lattices using linked-cluster methods. Simplifications for the bimodal distribution allow us…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
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…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…
An one-step replica-symmetry-breaking solution for finite connectivity spin-glass models with K body interaction is constructed at finite temperature using the replica method and thermodynamic constraints. In the absence of external fields,…
We introduce a novel method for numerical spin glass investigations: Simulations of two replica at fixed temperature, weighted such that a broad distribution of the Parisi overlap parameter $q$ is achieved. Canonical expectation values for…
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 consider a Lattice Gas model in which the sites interact via infinite-ranged random couplings independently distributed with a Gaussian probability density. This is the Lattice Gas analogue of the well known Sherrington-Kirkpatrick Ising…
We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical…
We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…
We study the dynamical low temperature behaviour of the Ising spin glass on the Bethe lattice. Starting from Glauber dynamics we propose a cavity like Ansatz that allows for the treatment of the slow (low temperature) part of dynamics.…
We consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory…
Spin systems with frustration and disorder are notoriously difficult to study both analytically and numerically. While the simulation of ferromagnetic statistical mechanical models benefits greatly from cluster algorithms, these accelerated…
The Ising spin-glasses are investigated on three dual pairs of hierarchical lattices, using exact renormalization-group transformation of the quenched bond probability distribution. The goal is to investigate a recent conjecture which…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
We construct a model of short-range interacting Ising spins on a translationally invariant two-dimensional lattice that mimics a reversible circuit that multiplies or factorizes integers, depending on the choice of boundary conditions. We…
The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent…
We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin…
The frustrated Ising model in two dimensions is revisited. The frustration is quantified in terms of the number of non-trivial plaquettes which is invariant under the Nishimori gauge symmetry. The exact ground state energy is calculated…
An approximate numerical approach to spin models is proposed, in which the original lattice is transformed into a tree. This method is applied to the Edwards-Anderson spin glass model in two and three dimensions. It captures the…