Monte Carlo simulation of size-effects on thermal conductivity in a 2-dimensional Ising system

TL;DR

This study uses Monte Carlo simulations to analyze how the size of a 2D Ising system affects its thermal conductivity, revealing size-dependent scaling behavior influenced by temperature.

Contribution

It introduces a microcanonical Monte Carlo approach to quantify size effects on thermal conductivity in 2D Ising systems, highlighting the size scaling law and magnetic field effects.

Findings

Thermal conductivity scales with system size as K=cL^α, with α depending on temperature.

Average demon energy is zero at low temperatures under an external magnetic field.

Both Metropolis and Cruetz algorithms effectively establish temperature gradients.

Abstract

A model based on microcanonical Monte Carlo method is used to study the application of the temperature gradient along a two-dimensional (2D) Ising system. We estimate the system size effects on thermal conductivity, $K$, for a nano-scale Ising layer with variable size. It is shown that $K$ scales with size as $ K=cL^\alpha$ where $\alpha$ varies with temperature. Both the Metropolis and Cruetz algorithms have been used to establish the temperature gradient. Further results show that the average demon energy in the presence of an external magnetic field is zero for low temperatures.