Partial entropy in finite-temperature phase transitions

TL;DR

This paper introduces the concept of partial entropy as a classical analogue of quantum entanglement entropy, demonstrating its effectiveness in analyzing finite-temperature phase transitions through finite-size scaling in classical models.

Contribution

It proposes partial entropy as a new tool for studying phase transitions and validates its utility on classical Ising and Heisenberg models.

Findings

Partial entropy exhibits perfect finite-size scaling near critical temperature.

Partial entropy effectively characterizes finite-temperature phase transitions.

The method applies to both classical Ising and Heisenberg models.

Abstract

It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect finite-size scaling behavior even for quite small system sizes. This provides a powerful tool to quantify finite-temperature phase transitions as demonstrated on the classical Ising model on a square lattice and the ferromagnetic Heisenberg model on a cubic lattice.