Static critical behavior of 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchan
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SORDER, AND PHASE TRANSITION IN CONDENSED SYSTEMS
Static Critical Behavior of 3D Frustrated Heisenberg Model on Stacked Triangular Lattice with Variable Interlayer Exchange Coupling A. K. Murtazaeva,b,*, M. K. Ramazanova,**, and M. K. Badieva a
Institute of Physics, Dagestan Scientific Center, Russian Academy of Sciences, Makhachkala, Republic of Dagestan, 367003 Russia b Dagestan State University, Makhachkala, 367025 Republic of Dagestan, Russia * e-mail: [email protected] ** e-mail: [email protected] Received June 7, 2007
Abstract—Several Monte Carlo algorithms are used to examine the critical behavior of the 3D frustrated Heisenberg model on stacked triangular lattice with variable interlayer exchange coupling for values of the interlayer-to-intralayer exchange ratio R = |J '/J | in the interval between 0.01 and 1.0. A finite-size scaling technique is used to calculate the static magnetic and chiral critical exponents α (specific heat), γ and γk (susceptibility), β and βk (magnetization), ν and νk (correlation length), and the Fisher exponent η. It is shown that 3D frustrated Heisenberg models on stacked triangular lattice with R > 0.05 constitute a new universality class of critical behavior. At lower R, a crossover from 3D to 2D critical behavior is observed. PACS numbers: 05.70.Fh, 75.40.Cx, 75.40.Mg DOI: 10.1134/S1063776107110131
1. INTRODUCTION Phase transitions and critical phenomena in frustrated spin systems are one of the most complicated and interesting research areas in statistical physics. The modern theory of phase transitions and critical phenomena is mostly based on the ideas underlying scaling hypotheses, universality, and renormalization group theory [1, 2]. Many results obtained in studies of frustrated systems and spin systems with quenched nonmagnetic disorder go far beyond the scope of the modern theory of phase transitions and critical phenomena [3]. Recent advances in understanding phase transitions and critical phenomena in frustrated systems have largely been achieved by applying computational physics methods, because most attempts to calculate the critical exponents and characterize the mechanisms of the critical behavior of such systems by conventional theoretical and experimental methods are confronted by serious difficulties [3, 4]. This stimulated the application of Monte Carlo (MC) methods to phase transitions and critical phenomena in frustrated systems [4– 11]. Analysis of the critical region by MC methods became possible only in recent years. As of today, the results of MC simulations are not inferior, and sometimes are even superior, to those obtained by other methods [4, 9]. These advances have been achieved not only by increasing the computing power of modern computers,
but also by using additional ideas and methods. With regard to frustrated systems, we primarily refer to replica-exchange Monte Carlo algorithms [12] and finitesize scaling ideas [5, 13–19]. Critical behavior of frustrated spin systems remains the subject of ongoing studies [20–23]. These systems exhibit many pr
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