Ising transition in the two-dimensional quantum $J_1-J_2$ Heisenberg model

Abstract

We study the thermodynamics of the spin-$S$ two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest ($J_1$) and next-nearest ($J_2$) neighbor couplings in its collinear phase ($J_2/J_1>0.5$), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio $J_2/J_1$ is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin- and temperature-dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li${}_2$VOSiO${}_4$ and related compounds.

arXiv comment4 page, 4 figures

References in corpus (14)

• Li${}_2$VO(Si,Ge)O${}_4$, a prototype of a two-dimensional frustrated quantum Heisenberg antiferromagnet
• Asymptotic scaling of the square lattice quantum Heisenberg antiferromagnet
• Magnetic and thermodynamic properties of Li(2)VOSiO(4): a two-dimensional S=1/2 frustrated antiferromagnet on a square lattice
• Ising transition driven by frustration in a 2D classical model with SU(2) symmetry
• Frustration driven structural distortion in VOMoO4
• Realization of a large J_2 quasi-2D spin-half Heisenberg system: Li2VOSiO4
• A closer look at symmetry breaking in the collinear phase of the $J_1-J_2$ Heisenberg Model
• Very low-frequency excitations in frustrated two-dimensional $S=1/2$ Heisenberg antiferromagnets
• Suppression of Dimer Correlations in the Two-Dimensional $J_1$-$J_2$ Heisenberg Model: an Exact Diagonalization Study
• Determination of the exchange energies in Li2VOSiO4 from a high-temperature series analysis of the square lattice J1-J2 Heisenberg model
• The two-dimensional quantum Heisenberg antiferromagnet: effective Hamiltonian approach to the thermodynamics
• Quantum Effects and Broken Symmetries in Frustrated Antiferromagnets
• Thermodynamics of the quantum easy-plane antiferromagnet on the triangular lattice
• Finite-size spin-wave theory of a collinear antiferromagnet

Cited by in corpus (31)

• Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions
• Pnictides as frustrated quantum antiferromagnet close to a quantum phase transition
• Symplectic N and time reversal in frustrated magnetism
• Low temperature broken symmetry phases of spiral antiferromagnets
• Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides
• Anisotropy-induced ordering in the quantum J1-J2 antiferromagnet
• Cluster Density Matrix Embedding Theory for Quantum Spin Systems
• Spin-waves in the $J_{1a}-J_{1b}-J_2$ orthorombic square-lattice Heisenberg models: Application to the iron pnictide materials
• Finite-temperature properties of frustrated classical spins coupled to the lattice
• Spin Dilution in Frustrated Two-Dimensional s=1/2 Antiferromagnets on a Square Lattice
• The Ising phase in the J1-J2 Heisenberg Model
• Effect of anisotropy on the ground-state magnetic ordering of the spin-one quantum $J_1^{XXZ}$--$J_2^{XXZ}$ model on the square lattice
• Tuning order-by-disorder multiferroicity in CuO by doping
• Emergent Critical Phase and Ricci Flow in a 2D Frustrated Heisenberg Model
• Emergent Potts Order in a Coupled Hexatic-Nematic XY model
• Thermal Ising transition in the spin-1/2 J1-J2 Heisenberg model
• Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice
• Emergent Criticality and Friedan Scaling in a 2D Frustrated Heisenberg Antiferromagnet
• Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment
• Weakly frustrated two-dimensional Heisenberg antiferromagnets: thermodynamic properties from a non-perturbative approach
• Diagnosing order by disorder in quantum spin systems
• A Magnetic Model of the Tetragonal-Orthorhombic Transition in the Cuprates
• Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model
• An Equilibrium for Frustrated Quantum Spin Systems in the Stochastic State Selection Method
• Broken discrete and continuous symmetries in two dimensional spiral antiferromagnets
• Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities
• Thermal Ising transition in two-dimensional SU(3) Fermi lattice gases with population imbalance
• The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A variational method study
• Cooper Pair Induced Frustration and Nematicity of Two-Dimensional Magnetic Adatom Lattices
• Two-orbital quantum spin model of magnetism in the iron pnictides
• Quantum Heisenberg antiferromagnets: a survey of the activity in Firenze