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Solid State Communications

Correlated effective field method in the location of the Ising model tricritical point

B. Frank, Meir Danino

Published Nov 1, 1985• 3 citations
Publisher
DOI
10.1016/0038-1098(85)90975-5

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Journal of Physics C Solid State Physics•Sep 10, 1986•82 citations
Quantum tricriticality of a ${J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnetic Ising model on a square lattice is studied using the mean-field (MF) theory, scaling theory, and the unbiased worldline quantum Monte-Carlo (QMC) method based on the Feynman path integral formula. The critical exponents of the quantum tricritical point (QTCP) and the qualitative phase diagram are obtained from the MF analysis. By performing the unbiased QMC calculations, we provide the numerical evidence for the existence of the QTCP and numerically determine the location of the QTCP in the case of J1=J2{J}_{1}={J}_{2}J1​=J2​. From the systematic finite-size scaling analysis, we conclude that the QTCP is located at HQTCP/J1=3.260(2){H}_{\mathrm{QTCP}}/{J}_{1}=3.260(2)HQTCP​/J1​=3.260(2) and ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{QTCP}}/{J}_{1}=4.10(5)$. We also show that the critical exponents of the QTCP are identical to those of the MF theory, because the QTCP in this model is in the upper critical dimension. The QMC simulations reveal that unconventional proximity effects of the ferromagnetic susceptibility appear close to the antiferromagnetic QTCP, and the proximity effects survive for the conventional quantum critical point. We suggest that the momentum dependence of the dynamical and static spin structure factors is useful for identifying the QTCP in experiments.