相关论文: Statistical mechanics approach to lattice field th…

The Mean Spherical Approximation (MSA) is a commonly-used thermodynamic theory for computing the energetics of ions in the primitive model (i.e., charged hard-sphere ions in a background dielectric). For the excess chemical potential,…

We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we…

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…

Many machine learning and optimization algorithms can be cast as instances of stochastic approximation (SA). The convergence rate of these algorithms is known to be slow, with the optimal mean squared error (MSE) of order $O(n^{-1})$. In…

The mean spherical approximation (MSA) can be solved semi-analytically for the Gaussian core model (GCM) and yields - rather surprisingly - exactly the same expressions for the energy and the virial equations. Taking advantage of this…

Mean-field approximation is often used to explore the qualitative behaviour of phase transitions in classical spin models before employing computationally costly methods such as the Monte-Carlo techniques. We implement a 'lattice…

Due to their broad applicability, gauge theories (GTs) play a crucial role in various areas of physics, from high-energy physics to condensed matter. Their formulations on lattices, lattice gauge theories (LGTs), can be studied, among many…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

Stochastic approximation (SA) that involves multiple coupled sequences, known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings…

Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and…

A family of spin-lattice models are derived as convergent finite dimensional approximations to the rest frame kinetic energy of a barotropic fluid coupled to a massive rotating sphere. In not fixing the angular momentum of the fluid…

The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a…

This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…

The reliability of the mean-field approach to polymer statistical mechanics is investigated by comparing results from a recently developed lattice mean-field theory (LMFT) method to statistically exact results from two independent numerical…

Simulations of extended quantum systems are typically performed by extrapolating results of a sequence of finite-system-size simulations to the thermodynamic limit. In the quantum Monte Carlo community, twist-averaging was pioneered as an…

In this paper we extend the familiar continuum electrostatic model with a perturbation to the usual macroscopic boundary condition. The perturbation is based on the mean spherical approximation (MSA), to derive a multiscale hydration-shell…

Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical…

Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal…

Symbolic data analysis (SDA) aggregates large individual-level datasets into a small number of distributional summaries, such as random rectangles or random histograms. The inference is carried out using these summaries in place of the…

A multi-chain mean-field theory is developed and applied to a two-dimensional system of weakly coupled S=1/2 Heisenberg chains. The environment of a chain C_0 is modeled by a number of neighbor chains C_d, d = +/-1,...,+/-n, with the edge…