Related papers: Canonical local algorithms for spin systems: Heat …
We introduce a novel framework for simulating spin models using differentiable programming, an approach that leverages the advancements in machine learning and computational efficiency. We focus on three distinct spin systems: the Ising…
Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we…
We describe a number of recently developed cluster-flipping algorithms for the efficient simulation of classical spin models near their critical temperature. These include the algorithms of Wolff, Swendsen and Wang, and Niedermeyer, as well…
A cluster algorithm is presented for the simulation of the q-state Potts models in which the number of spins is conserved in each state. The algorithm constructs Fortuin-Kasteleyn cluster configurations from spin configurations, in a way…
We propose a new local algorithm for the thermalization of n-vector spin models, which can also be used in the numerical simulation of SU(N) lattice gauge theories. The algorithm combines heat-bath (HB) and micro-canonical updates in a…
We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
Various combinatorial optimization NP-hard problems can be reduced to finding the minimizer of an Ising model, which is a discrete mathematical model. It is an intellectual challenge to develop some mathematical tools or algorithms for…
Optical simulators for the Ising model have demonstrated great promise for solving challenging problems in physics and beyond. Here, we develop a spatial optical simulator for a variety of classical statistical systems, including the clock,…
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…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…
Dynamical Ising machines are continuous dynamical systems that evolve from a generic initial state to a state strongly related to the ground state of the classical Ising model. We show that such a machine driven by the V${}_2$ dynamical…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
Recently, several platforms were proposed and demonstrated a proof-of-principle for finding the global minimum of the spin Hamiltonians such as the Ising and XY models using gain-dissipative quantum and classical systems. The implementation…
Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the…
Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…
We study Bosonic representation of spin Ising model with the application of simulating two level systems using continuous variable quantum processors. We decompose the time evolution of spin systems into a sequence of continuous variable…
The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have…
Finding the ground states of the Ising Hamiltonian [1] maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence, and social network. So far no efficient classical and quantum…