Multi-spin exchange model the near melting transition of the 2D Wigner crystal

TL;DR

This paper investigates the validity and convergence of the multi-spin exchange model near the melting transition of a 2D Wigner crystal, using Path Integral Monte Carlo simulations to compute exchange energies and analyze magnetic properties.

Contribution

It provides a detailed assessment of the multi-spin exchange model's convergence and the applicability of Thouless theory near the melting point of the 2D Wigner crystal.

Findings

Exchange energies increase near melting transition.

Model fits and extrapolations suggest convergence of the multi-spin exchange model.

Results inform on magnetic susceptibility and specific heat contributions.

Abstract

The low temperature properties of fermionic solids are governed by spin exchanges. Near the melting transition, the spin-exchange energy increases as well as the relative contribution of large loops. In this paper, we check the convergence of the multi-spin exchange model and the validity of the Thouless theory near the melting of the Wigner crystal in two dimensions. Exchange energies are computed using Path Integral Monte Carlo for loop sizes up to 8, at $r_s=40$, 50 and 75. The data are then fitted to a geometric model. Then the exchange energies are extrapolated to larger sizes in order to evaluate their contributions to the leading term of the magnetic susceptibility and the specific heat. These results are used to check the convergence of the multi-spin exchange model.