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Theoretical and Mathematical Physics

Fluctuation phenomena in the tricritical behavior of two models with tensor order parameter

Andrey V. Smirnov, B. A. Storonkin

Published Aug 1, 1985• 0 citations
Publisher
DOI
10.1007/bf01017967

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The fluctuations of massless Dirac fermion can not only turn a first-order bosonic phase transition (in the Landau sense) to a quantum critical point, but also work reversely to enhance the first-order transition itself, depending on the implementation of finite-size effects in the coupling corrections. Here, we report a case study of the latter by employing quantum Monte Carlo simulation upon a lattice model in which the bosonic part featuring the Landau-Devonshire first-order phase transition and Yukawa coupled to the Dirac fermions. We find that the parameter range for the first-order phase transition becomes larger as the Yukawa coupling increases, and the microscopic mechanism of this phenomena is revealed, at a quantitative level, as the interplay between the critical fluctuations and the finite-size effects. Moreover, the scaling behavior at the separation point between the first-order and the continuous phase transitions is found to belong to the chiral tricritical Gross-Neveu universality. Our results demonstrate that the interplay of massless Dirac fermions, critical fluctuations, and the finite-size effects could trigger a plethora of interesting phenomena, and therefore great care is called for when making generalizations.
In finite-size thermal systems that exhibit second-order phase transition, the fluctuations of the order parameter ϕn obey type I intermittent dynamics at their pseudocritical temperature Tpc . Moreover, as recently demonstrated, spontaneous symmetry breaking (SSB) is gradually completed as temperature is reduced until reaching an SSB completion temperature, TSSB . Within this temperature zone, ϕn obey the dynamics of critical intermittency. This behavior has also been observed in pre-seismic fracture-induced electromagnetic emissions (FEME) of the MHz band—a real-world finite-size system undergoing a second-order phase transition. Interestingly, MHz FEME has recently been found to consistently present indications of tricritical dynamics after the SSB. We examine here whether this could also be true for a finite-size thermal system. We conduct a numerical experiment for the 3D Ising model at different temperatures by gradually reducing temperature beyond SSB and analyze order parameter fluctuations using the method of critical fluctuations (MCF) and a recently introduced wavelet-based method for detecting scaling behavior in noisy experimental data. Our results reveal that power-laws still exist within a very narrow zone of temperatures right after SSB completion for the 3D Ising model. These power-laws are shown to be compatible with another form of intermittency that determines the dynamics of the order parameter fluctuations close to the Griffiths tricritical point. As a possible interpretation of this finding, we suggest that our results imply that 3D Ising presents, just below TSSB , an imprint approaching the Griffiths tricritical point from the second-order phase transition line.
Quantum tricriticality, a unique form of high-order criticality, is expected to exhibit fascinating features including unconventional critical exponents and universal scaling laws. However, a quantum tricritical point (QTCP) is much harder to access, and the corresponding phenomena at tricriticality have rarely been investigated. In this study, we explore a tricritical quantum Rabi model, which incorporates a nontrivial parameter for adjusting the coupling ratio between a cavity and a three-level atom. The QTCP emerges at the intersection of a first- and second-order superradiant phase transitions according to Landau theory. By using finite-frequency scaling analyses for quantum fluctuations and the mean photon number, universal critical exponents differentiate the QTCP from the second-order critical point. We find that the phase transition at the tricritical point goes beyond the conventional second-order phase transition. Our work explores an interesting direction in the generalization of the well-known Rabi model for the study of higher-order critical points due to its high control and tunability.