Investigation of frustrated and dimerized classical Heisenberg chains

TL;DR

This paper maps the classical phase diagram of 1D dimerized frustrated Heisenberg chains, revealing rich phase transitions, including first and second-order, and analyzing the stability of spiral order near critical points.

Contribution

It provides the exact classical phase diagram for dimerized frustrated Heisenberg chains using the LK cluster method, highlighting new phase transition features and spiral order stability.

Findings

Second-order transition at critical frustration $ ext{α}_c=±0.25$

Existence of first-order critical lines separating phases

Stability of spiral order in dimerized chains

Abstract

We have considered the 1D dimerized frustrated antiferromagnetic (ferromagnetic) Heisenberg model with arbitrary spin $S$. The exact classical magnetic phase diagram at zero temperature is determined using the LK cluster method. Cluster method results, show that the classical ground state phase diagram of the model is very rich including first and second-order phase transitions. In the absence of the dimerization, a second-order phase transition occurs between antiferromagnetic (ferromagnetic) and spiral phases at the critical frustration $\alpha_c=\pm 0.25$. In the vicinity of the critical points $\alpha_c$, the exact classical critical exponent of the spiral order parameter is found 1/2. In the case of dimerized chain ($\delta\neq0$), the spiral order shows stability and exists in some part of the ground state phase diagram. We have found two first-order critical lines in the ground state phase diagram. These critical lines separate the antiferromagnetic from spiral phase.