Estudo do modelo XY por Monte Carlo - Marcelo de Oliveira Silva Guimaraes (2014)
Phase transitions in spins systems offers perspectives in understanding low tempera- ture critical behavior of matter. In this work we applied the Stochastic Series Expansion method to study the critical properties of antiferromagnetic coupled spins during a quan- tum phase transition mediated by an anisotropy term. We simulated the tridimensional XY model with easy plane anisotropy D, for spins S = 1,3/2 and 2 in cubic lattices (L x L x L) with periodic boundary conditions for L 2 [4,24] . The quantum phase transition is characterized by the change of the ground state of the system due to an increase in that parameter. For semi-integer spins, the increase in this anisotropic term restrict the acessible spin space of each spin to that of S = 1/2, which only adds a trivial constant to the system energy, therefore no change in the ground state is expected. For integer spins we have a different case. For small D the sistem is found to be in a gapless phase. For small D and high temperature the magnetic ordering is destroied by thermic fluctuations. For large D and T = 0 the system has a unique ground state with Sztotal = 0 , and its first excited state is found in the magnetization sector Sztotal = 1 defined by an energy gap. The quantum critical point is determined precisely in this work, which coincide with the analytical results obtained by Pires e Costa[1]. The dynamic correlation lenght critical properties were calculated. The dynamical critical exponent z ( which governs the relation between the espacial and temporal correlation length), was obtained using an ansatz to the low temperature magnetic susceptibility behavior. The high D gap was estimated and the critical exponent z = 0.59(1) was found. Using finite size scaling, we constructed the phase diagram of the model and obtained the critical exponent z = 0.501(5), the critical point Dc = 9.7948(3)J for spin 1 and z = 0.498(2) , Dc = 29.923(5)J for spin 2. No quantum phase transition was observed for S = 3/2 as expected. The critical exponent was obtained by a similar relation used in Ref[2] and using a judicious procedure developed by me.