Stationary Metastability in an Exact Non-Mean Field Calculation for a Model without Long-Range Interactions

TL;DR

This paper introduces stationary metastable states (SMS) in a 1D spin model without long-range interactions, using an exact solution and analytic continuation to explore metastability beyond mean-field approximations.

Contribution

It provides an exact calculation demonstrating SMS existence in a non-mean-field, short-range interaction model, challenging the notion that metastability requires long-range forces.

Findings

SMS can be studied via restricted partition functions and free energy continuation.

A phase transition occurs at m<1, with metastable states represented below the transition.

The approach shows metastability is not exclusive to mean-field or long-range interaction models.

Abstract

We introduce the concept of stationary metastable states (SMS's) in the presence of another more stable state. The stationary nature allows us to study SMS's by using a restricted partition function formalism as advocated by Penrose and Lebowitz and requires continuing the free energy. The formalism ensures that SMS free energy satisfies the requirement of thermodynamic stability everywhere including T=0, but need not represent a pysically observable metastable state over the range where the entropy under continuation becomes negative. We consider a 1-dimensional m-component axis-spin model involving only nearest-neighbor interactions, which is solved exactly. The high-temperature expansion of the model representys a polymer problem in which m acts as the activity of a loop formation. We follow deGennes and trerat m as a real variable. A thermodynamic phase transition occurs in the model for m<1. The analytic continuation of the high-temperature disordered phase free energy below the transition represents the free energy of the metastable state. The calculation shows that the notion of SMS is not necessaily a consequence of only mean-field analysis or requires long-range interactions.