# Squeezed ensemble for systems with first-order phase transitions

## TL;DR

This paper introduces a new class of statistical ensembles, called squeezed ensembles, that accurately describe systems with first-order phase transitions, especially finite systems, improving computational efficiency and reducing finite-size effects.

## Contribution

The paper proposes and derives a new class of ensembles that remain valid in the first-order transition region and are practical for finite systems, with formulas relating different ensembles.

## Key findings

- Squeezed ensembles accurately capture equilibrium states in first-order transitions.
- Formulas relate different ensembles, reducing finite-size effects.
- Application to models confirms advantages of the new ensembles.

## Abstract

All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition region, one must choose an appropriate statistical ensemble. The appropriate choice is particularly important when one investigates finite systems, for which even the equivalence of ensembles does not hold. We propose a class of statistical ensembles, which always give the correct equilibrium state even in the first-order phase transition region. We derive various formulas for this class of ensembles, including the one by which temperature is obtained directly from energy without knowing entropy. Moreover, these ensembles are convenient for practical calculations because of good analytic properties. We also derive formulas which relate statistical-mechanical quantities of different ensembles, including the conventional ones, for finite systems. The formulas are useful for obtaining results with smaller finite-size effects, and for improving the computational efficiency. The advantages of the squeezed ensembles are confirmed by applying them to the Heisenberg model and the frustrated Ising model.