Phase transitions in 2D $J_{1}-J_{2}$ model with arbitrary signs of exchange interactions

TL;DR

This paper investigates phase transitions in the 2D $J_{1}-J_{2}$ Heisenberg model with arbitrary exchange signs, revealing the nature of various ordered and disordered states and characterizing the transition types.

Contribution

It introduces a unified analytical approach to describe multiple spin states and phase transitions in the 2D $J_{1}-J_{2}$ model with arbitrary exchange interactions.

Findings

Second-order phase transition between ferromagnetic spin liquid and ferromagnetic order.

Identification of ferromagnetic states with rapidly varying condensate functions.

Description of various long-range order and disordered spin-liquid states.

Abstract

The ground state of the $S=1/2$ $J_{1}-J_{1}$ Heisenberg model on the 2D square lattice with arbitrary signs of exchange constants is considered. States with different spin long-range order types (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as disordered spin-liquid states are described in the frames of one and the same analytical approach. It is shown inter alia, that the phase transition between ferromagnetic spin liquid and long-range order ferromagnet is a second-order one. On the ordered side of the transition the ferromagnetic state with rapidly varying condensate function is detected.