The spin-glass phase in the LiHoxY1−xF4 compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J =...

We investigate phase transitions in the Ising model and the ANNNI model in transverse field using the interface approach. The exact result of the Ising chain in a transverse field is reproduced. We find that apart from the interfacial energy, there are two other response functions which show simple scaling behaviour. For the ANNNI model in a transverse field, the phase diagram can be fully stud...

We formulate a cluster Monte Carlo method for the anisotropic limit of Ising models on (d+1)-dimensional lattices, which in effect, are equivalent with d-dimensional quantum transverse Ising models. Using this technique, we investigate the transverse Ising models on the square, triangular, Kagome, honeycomb, and simple-cubic lattices. The Monte Carlo data are analyzed by finite-size scaling. In...

We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Mean field theory, application to superconductivity by BCS and real space renormalization group technique (in one dimension) are discussed. Next we introduce Suzuki-Trotter formalism to show the correspondence between d-dimensional quantum system with a (d + 1)-dimensional classical system. We then d...

This paper will review recent results on the finite temperature (T ) properties of the one-dimensional Ising chain in a transverse field. The discussion here is a synthesis of two recent papers1,2 by the author to which the reader is referred for further details. Further work on the one-dimensional Ising model appears in a recent paper3 and will not be reviewed here. We will also not consider p...

We show that a class of exactly solvable quantum Ising models, including the transverse-field Ising model and anisotropic XY model, can be characterized as the loops in a two-dimensional auxiliary space. The transverse-field Ising model corresponds to a circle and the XY model corresponds to an ellipse, while other models yield cardioid, limacon, hypocycloid, and Lissajous curves etc. It is sho...