Abstract

Monte Carlo simulations have boosted the numerical study of several different physical systems and in particular, the canonical ensemble has been especially useful because of the existence of easy and efficient simulation algorithms. Nevertheless, nature does not know about statistical ensembles and therefore it is desirable and a theoretical challenge to show how to perform numerical simulations in the microcanonical ensemble without the use of unphysical degrees of freedom. In this article, we present a straightforward applicable method based on the concepts of a configurational temperature estimator (Rugh Phys Rev Lett 78:772, 1997; Gutiérrez et al. J Phys A Math Theor 51:455003, 2018) and on stochastic dynamics, which is independent of the Monte Carlo update strategy, and can be implemented for both local update or cluster algorithms. We illustrate it by performing a numerical simulation of the two-dimensional XY-model, finding the equilibrium temperature of two spin subsystems initially at different temperatures when they are put into thermal contact.

Graphic abstract

中文翻译：

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使用蒙特卡洛模拟对微规范集合中的系统进行采样的一般方法

摘要

蒙特卡洛模拟促进了几种不同物理系统的数值研究，特别是由于存在简单有效的模拟算法，规范合奏特别有用。然而，自然界并不了解统计合奏，因此，在不使用非物理自由度的情况下，如何在微经典合奏中进行数值模拟是可取的，也是理论上的挑战。在本文中，我们基于配置温度估算器的概念（Rugh Phys Rev Lett 78：772，1997;Gutiérrez等人，J Phys A Math Theor 51：455003，2018）和随机动力学提出了一种简单易用的适用方法，它独立于Monte Carlo更新策略，并且可以针对本地更新或集群算法实现。

图形摘要