Related papers: A gauge invariant cluster algorithm for the Ising …
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
An exact algorithm is used to compute the degeneracies of the excited states of the bimodal Ising spin glass in two dimensions. It is found that the specific heat at arbitrary low temperature is not a self-averaging quantity and has a…
A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical…
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…
Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed…
Thermodynamic and magnetocaloric properties of geometrically frustrated Ising spin clusters of selected shapes and sizes are studied by exact enumeration. In the ground state the magnetization and the entropy show step-wise variations with…
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
The critical exponents for $T\to0$ of the two-dimensional Ising spin glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to $L=50$ and by a Monte Carlo study of a pseudo-ferromagnetic…
We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for…
A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum…
We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We…
We use Monte Carlo (MC) methods to simulate a two-dimensional (2D) bond-diluted Ising model on the square lattice which has frustration between the nearest-neighbor interaction J1 and the next-nearest-neighbor interaction J2. In this paper,…
We conjecture the existence of a relationship between frustration and the transition point at zero temperature of Ising spin glasses. The relation reveals that, in several Ising spin glass models, the concentration of ferromagnetic bonds is…
The magnetic critical properties of two-dimensional Ising spin glasses are controversial. Using exact ground state determination, we extract the properties of clusters flipped when increasing continuously a uniform field. We show that these…
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…
A method is presented, which allows to sample directly low-temperature configurations of glassy systems, like spin glasses. The basic idea is to generate ground states and low lying excited configurations using a heuristic algorithm. Then,…
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 exchange or geometric cluster algorithm allows us to define a variance reduced estimator of the connected two-point function in the presence of a broken Z_2-symmetry. We present first numerical tests for the improved Blume-Capel model…
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…
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with…