# Thermodynamic Stability - A note on a footnote in Ruelle's book

## TL;DR

This paper presents new examples of thermodynamically stable interaction potentials in one and two dimensions, expanding the understanding of stability conditions beyond traditional forms using elementary methods.

## Contribution

It introduces novel stable interaction potentials not of the standard form, with explicit constructions in one and two dimensions, using elementary calculations.

## Key findings

- New stable interaction potentials in one dimension.
- Sketch of construction in two dimensions.
- Elementary calculation methods used for construction.

## Abstract

Thermodynamic stable interaction pair potentials which are not of the form ``positive function + real continuous function of positive type'' are presented in dimension one. Construction of such a potential in dimension two is sketched. These constructions use only elementary calculations. The mathematical background is discussed separately.