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Springer eBooks

Universality away from critical points in a thermostatistical model

Cintia Mariela Lapilli, Carlos Wexler, Peter Pfeifer

Published Jan 1, 2010• 0 citations
Publisher
DOI
10.1007/978-3-540-85081-6_55

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Recently, the ordering scenario of three-dimensional site frustrated Heisenberg models has been challenged. The existence of a decoupled tetracritical point (DTP) where ferromagnetic (FM) and antiferromagnetic (AF) order occur simultaneously has been modified to include a line of multicritical points where both FM and AF occur simultaneously. In addition, numerous studies claim that, within the mixed phase, critical exponents are altered from Heisenberg values. Here we show that within the narrow region of proposed multicritical points, the transition temperatures away from the tetracritical point are indeed distinct, confirming the occurrence of a DTP. In addition, we show a universal scaling collapse of the magnetization both away from, and within, the mixed phase using Heisenberg exponents, demonstrating that the stable fixed points are within the Heisenberg universality class.
Emergent symmetry is one of the characteristic phenomena in deconfined quantum critical points (DQCP). As its nonequilibrium generalization, the dual dynamic scaling was recently discovered in the nonequilibrium imaginary-time relaxation dynamics in the DQCP of the $J\text{\ensuremath{-}}{Q}_{3}$ model. In this paper, we study the nonequilibrium imaginary-time relaxation dynamics in the $J\text{\ensuremath{-}}{Q}_{2}$ model, which also hosts a DQCP belonging to the same equilibrium universality class. We not only verify the universality of the dual dynamic scaling at the critical point but also investigate the breakdown and the vestige of the dual dynamic scaling when the tuning parameter is away from the critical point. We also discuss possible experimental realizations in devices of quantum computers.
Within the generalized thermostatistics of Tsallis, we propose for the spin-12 Ising ferromagnet a transmissivity variable which extends that defined by Tsallis and Levy for thermal magnetic systems. By using this generalized transmissivity as well as duality arguments, we calculate the q-dependence of the critical temperature corresponding to the square lattice, where q is the entropic index (q = 1 reproduces standard thermostatistics). Our approximate results are compared with those previously obtained using renormalization group and mean-field approximation.