Nontopological thermal solitons in isotropic ferromagnetic lattices

TL;DR

This paper develops an exact statistical mechanics framework for thermally excited solitons in isotropic ferromagnetic chains, revealing their thermodynamic behavior across different temperature and field regimes, and comparing with known models.

Contribution

It introduces a comprehensive analytical approach to describe the thermodynamics of interacting solitons in ferromagnetic chains for various limits, including classical and quantum regimes.

Findings

Thermodynamics matches the Heisenberg model at low temperatures.

Analytical approximations describe soliton energy behavior in different limits.

Results agree with transfer integral and Bethe-Ansatz methods in respective regimes.

Abstract

The paper deals with the properties of thermally excited solitons of the isotropic spin-$S$ ferromagnetic chain with nearest-neighbor logarithmic interactions. The exact statistical mechanics of the interacting soliton gas is developed for the general case (arbitrary $S$, temperature and magnetic field). At low temperatures the model's thermodynamics coincides with that of the Heisenberg model. We present analytical approximations of the leading-order asymptotic behavior of the energy in three limiting cases: (a) zero field, low temperature, classical limit; (b) zero field, $T\to 0$, $S$ finite (quantum limit); (c) zero field, high temperature, classical limit. Cases (a) and (c) are examples of a dense gas of [non-topological] solitons; results are in agreement with those obtained by the transfer integral method. Case (b) illustrates the behavior of a dilute, yet strongly interacting soliton gas; results for the thermodynamics are very close to (but not identical with) spin-wave and/or Bethe-{\it Ansatz} predictions.