Monte Carlo method for the Ising model in a transverse field

Phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field

“…Theoretically, various methods has been employed to study the criticality of the TIM such as renormalizaton group (RG) method [6], effective field theory (EFT) [7][8][9], mean field theory (MFA) [10], cluster variation method (CVM) [11], pair approximation (PA) [12], Monte Carlo (MC) simulations [13], and so on. The critical behavior of the one dimensional TIM has already been established through exact results, where the ground-state energy, the elementary excitations and the correlation functions were obtained [14].…”

“…Monte Carlo (MC) simulations [13], and so on. The critical behavior of the one dimensional TIM has already been established through exact results, where the ground-state energy, the elementary excitations and the correlation functions were obtained [14].…”

“…From a theoretical point of view it is known that the effect of the transverse field in the Ising model TIM is to destroy the long-range order of the system. Many approximate methods [6][7][8][9][10][11][12][13][20][21][22][23][24][25][26][27][28][29] have been used to study the critical properties of this quantum model. Some years ago, a simple and versatile scheme, denoted by differential operator technique [30], was proposed and has been applied exhaustively to study a large variety of problems.…”

An introduced effective-field theory study of spin-1 transverse Ising model with crystal field anisotropy in a longitudinal magnetic field

“…Details of calculation through (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) can be found in Appendix section. With the help of equations ( 6) and ( 7) the functions F (x), G(x), H(x) and K(x) in equations ( 8), ( 9), ( 14) and ( 15) can be calculated numerically from the relations…”

“…Following studies has been predicated that this semi-quantum mechanical model can be successfully applied to a variety of physical systems such as DyV O 4 , T bV O 4 [2] and some real magnetic materials [3]. From the theoretical point of view, transverse Ising model (TIM) has been investigated by a variety of techniques such as renormalization group method (RG) [4], effective field theory (EFT) [5][6][7], cluster variation method (CVM) [8], mean field theory (MFT) [9], pair approximation (PA) [10] and Monte Carlo simulations (MC) [11]. In the previous works mentioned above, the authors focused their attention on the behavior of tricritical points but have not considered the effect of the crystal field (i.e.…”