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In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…
We describe a numerical algorithm for computing spin glass ground states with a high level of reliability. The method uses a population based search and applies optimization on multiple scales. Benchmarks are given leading to estimates of…
Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an…
In quantum spin systems obeying hyperscaling, the probability distribution of the total magnetization takes on a universal scaling form at criticality. We obtain this scaling function exactly for the ground state and first excited state of…
The one-parameter scaling theory of localization predicts that all states in a disordered two-dimensional system with broken time reversal symmetry are localized even in the presence of strong spin-orbit coupling. While at constant strong…
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator…
We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip…
With the help of a smooth scaling and coarse-graining approach of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) we perform a rigorous renormalisation group…
All ground states and low-lying excitations of a +/- I Ising spin glass model on a cubic 4 x 4 x 4 lattice with periodical boundary conditions were calculated using a method of combinatorical optimization. The structure of states in the…
Energy minimization of Ising spin-glasses has played a central role in statistical and solid-state physics, facilitating studies of phase transitions and magnetism. Recent proposals suggest using Ising spin-glasses for non-traditional…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
The critical behaviour of the randomly spin-diluted Ising model in two space dimensions is investigated by a new method which combines a grand ensemble approach to disordered systems proposed by Morita with the phenomenological…
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi- infinite…
The `lid' algorithm performs an exhaustive exploration of neighborhoods of local energy minima of energy landscapes. This paper describes an implementation of the algorithm, including issues of parallel performance and scalability. To…
Around a glass transition, the dynamics of a supercooled liquid dramatically slow down, exhibited by caging of particles, while the structural changes remain subtle. In alternative to recent machine learning studies searching for structural…
Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in…
An efficient Monte Carlo method is extended to evaluate directly domain-wall free-energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model under…