This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the model in the parameters of inverse temperature and transverse field strength. Further analysis computes the critical exponent for the decay of the order paramete...

Using continued fractions we study the ground state properties of the spin– 1 2 Ising chain in a transverse field with periodically varying interaction strengths and external fields. We consider in detail the chain having the period of modulation of interactions equals 2 and compare the results obtained with those corresponding to the spin– 1 2 isotropic XY chain in a transverse field. In contr...

The contact model for the spread of disease may be viewed as a directed percolation model on Z×R in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly complete analysis of the contact model at and near its critical point. The corresponding process when the time-axis is unoriented is an undirected percolation model to which...

We derive a generic bound on the rate of decrease transverse field for quantum annealing to converge ground state Ising model when is formulated as an infinite-time process. Our theorem based rigorous upper excitation probability in limit and mathematically counterpart previously known result derived only from leading-order term asymptotic expansion adiabatic condition. Since our gives sufficie...

The classical, thermally driven transition in the dipolar-coupled Ising ferromagnet LiHoF 4 sTc ­ 1.53 Kd can be converted into a quantum transition driven by a transverse magnetic field Ht at T ­ 0. The transverse field, applied perpendicular to the Ising axis, introduces channels for quantum relaxation, thereby depressing Tc . We have determined the phase diagram in the Ht-T plane via magneti...

the coherent anomaly method and a cluster mean-field approach combined with finite-sizescaling extrapolation were used to determine the critical temperature and the critical exponents of as =1 ising chain with a long-range interaction in the form of 1/ r1+σ . the results of criticaltemperature are in good agreement with the recent results of the finite-range scaling method and aremore accurate ...

We use a simple real-space renormalization-group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspe...

Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. T...

We review the theoretical behaviour of the total and one-particle structure factors at a quantum phase transition for temperature T = 0. The predictions are compared with exact or numerical results for the transverse Ising model, the alternating Heisenberg chain, and the bilayer Heisenberg model. At the critical wavevector, the results are generally in accord with theoretical expectations. Away...

We consider a one-dimensional Ising model in a transverse magnetic field coupled to a dissipative heat bath. The phase diagram and the critical exponents are determined from extensive Monte Carlo simulations. It is shown that the character of the quantum phase transition is radically altered from the corresponding nondissipative model and the double well coupled to a dissipative heat bath with ...