Ising model in the R\'{e}nyi statistics: the finite size effects

TL;DR

This paper explores finite size effects in the 1D Ising model using Rényi statistics, deriving key thermodynamic parameters and revealing possible entropic phase transitions across a broad temperature range.

Contribution

It introduces a self-consistent method to relate Rényi $q$-index and system temperature to physical temperature, highlighting finite size effects and phase transitions.

Findings

Derivation of Rényi $q$-index and temperature from finite systems

Identification of entropic phase transitions in the model

Analysis of size effects on thermodynamic properties

Abstract

The R\'{e}nyi statistics is applied for a description of finite size effects in the 1D Ising model. We calculate the internal energy of the spin chain and the system temperature using the R\'{e}nyi distribution and postulate them to be equal to their counterparts, obtained in the microcanonical ensemble. It allows us to self-consistently derive the R\'{e}nyi $q$-index and the Lagrange parameter $T$ to relate them to the physically observed system temperature $T_{\rm ph}$, and to show that the entropic phase transitions are possible in a broad temperature domain. We have also studied the temperature dependence of the internal energy $U(T_{\rm ph})$ at constant $q$ and an influence of the size related effects on the system thermodynamics.