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Leandro G. Rizzi and Nelson A. Alves
Several studies to determine the nature of the thermodynamic phase transitions for an Ising model for ultrathin magnetic films have been reported in recent years. No conclusive results have been obtained yet, because the simulation with conventional Monte Carlo methods is slowed down by long relaxation times due to the suppression of tunneling events through free energy barriers. In this paper we study the Ising model with dipolar interactions in two dimensions with an generalized-ensemble algorithm to address this problem. Herein, the multicanonical algorithm has been implemented in this work because it systematically explores energy configurations and enhances the rate of tunneling events. The success of a simulation depends on how often the algorithm explores the energy range between two extremal values. Our results indicate a limitation of the multicanonical algorithm in estimating the density of states for this model because the algorithm does not satisfactorily circumvent the problem of high free energy barriers in the energy region where the nematic phase takes place.
computational physics and chemistry, multicanonical algorithm, dipolar Ising model, free-energy barrier.
 LANDAU DP & BINDER K. 2000. A guide to Monte Carlo simulations in Statistics Physics. Cambridge University Press.
 SWENDSEN RH & WANG J-S. 1987. Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett., 58: 86-88.
 KANDEL D, DOMANY E & BRANDT A. 1989. Simulations without critical slowing down: Ising and three-state Potts model. Phys. Rev. B, 40: 330-344.
 SALAS J & SOKAL AD. 1997. Dynamic critical behavior of the Swendsen-Wang algorithm: the two-dimensional three-state Potts model revisited. J. Stat. Phys., 87: 1-36.
 MITSUTAKE A, SUGITA Y & OKAMOTO Y. 2001. Generalizedensemble algorithms for molecular simulations of biopolymers. Biopolymers, 60: 96-123.
 BERG BA & CELIK T. 1992. New approach to spin-glass simulations. Phys. Rev. Lett. 69: 2292-2295.
 BERG BA, HANSMANN U & CELIK T. 1994. Ground-state properties of the three-dimensional Ising spin glass. Phys. Rev. B, 50: 16444-16452.
 GROSSMANN B, LAURSEN ML, TRAPPENBEG T & WIESE UJ. 1992. A multicanonical algorithm for SU(3) pure gauge theory. Phys. Lett. B, 293: 175-180.
 GROSSMANN B & LAURSEN ML. 1993. The confined-deconfined interface tension in quenched QCD using the histogram method. Nucl. Phys. B, 408: 637-656.
 SCHNABEL S, JANKE W & BACHMANN M. 2011. Advanced multicanonical Monte Carlo methods for efficient simulations of nucleation processes of polymers. J. Comp. Biol., 230: 4454- 4465.
 DEBELL K, MacISAAC AB & WHITEHEAD JP. 2000. Dipolar effects in magnetic thin films and quasi-two-dimensional systems. Rev. Mod. Phys., 72: 225-257.
 PORTMANN O, VATERLAUS A & PESCIA D. 2006. An inverse transition of magnetic domain patterns in ultrathin films. Nature, 422: 701-704; Observation of stripe mobility in a dipolar frustrated ferromagnet. Phys. Rev. Lett., 96: 047212 (2006).
 PZIGHIN S & CANNAS SA. 2007. Phase diagram of an Ising model for ultrathin magnetic films: Comparing mean field and Monte Carlo predictions. Phys. Rev. B, 75: 224-433.
 BOOTH I, MacISAAC AB, WHITEHEAD JP & DEBELL K. 1995. Domain structures in ultrathin magnetic films. Phys. Rev. Lett., 75: 950-953.
 ARLETT J, WHITEHEAD JP, MacISAAC AB & DEBELL K. 1996. Phase diagram for the striped phase in the two-dimensional dipolar Ising model. Phys. Rev. B, 54: 3394-3402.
 CANNAS SA, MICHELON MF, STARIOLO DA & TAMARIT FA. 2006. Ising nematic phase in ultrathin magnetic films: A Monte Carlo study. Phys. Rev. B, 73: 184425.
 RIZZI LG & ALVES NA. 2010. Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions. Physica B, 405: 1571-1579.
 CANNAS SA, MICHELON MF, STARIOLO DA & TAMARIT FA. 2008. Interplay between coarsening and nucleation in an Ising model with dipolar interactions. Phys. Rev. B, 78: 051602.
 BERG BA & NEUHAUS T. 1991. Multicanonical algorithms for first order phase transitions. Phys. Lett. B, 267: 249-253.
 BERG BA. 2000. Introduction to multicanonical Monte Carlo simulations. Fields Inst. Commun., 26: 1-24.
 BERG BA. 2003. Multicanonical simulations step by step. Comp. Phys. Comm., 153: 397-406.
 TOUKMAJI AY & BOARD Jr JA. 1996. Ewald summation techniques in perspective: a survey. Comput. Phys. Commun., 95: 73- 92; GAO GT, ZENG XC &WANGW, 1996. Vapor-liquid coexistence of quasi-two-dimensional Stockmayer fluids. J. Chem. Phys., 106: 3311-3317.
 RASTELLI E, REGINA S & TASSI A. 2007. Phase diagram of a square Ising model with exchange and dipole interactions: Monte Carlo simulations. Phys. Rev. B, 76: 054438.
 GROSS DHE. 2001. Microcanonical thermodynamics: phase transitions in small systems. World Scientific Publishing.
 SINHA S&ROY SK. 2009. Performance ofWang-Landau algorithm in continuous spin models and a case study: modified XY-model. Phys. Lett. A, 373: 308-314; 2010. Finite size scaling and firstorder phase transition in a modified XY model. Phys. Rev. E, 81: 022102.