Gene Stanley's early contribution to the n-vector model is briefly reviewed. Also discussed is a problem solved by McCrea and Whipple in 1940; namely random walks with absorbing boundaries. We have found the exact solution of the analogous problem on the triangular lattice with a true finite...

We investigate phase transitions of the XY model on a two-layer triangular lattice when interactions are competing, by using Monte Carlo simulations. For the system with a ferromagnetic interaction on one of two layers and an antiferromagnetic interaction on the other layer, we find two...

In this paper we study the quantum phase transition and low temperature behavior in a square lattice quantum two-dimensional XY model with single-ion anisotropy and spin S=1. Starting with the Villain representation, a Landau–Ginzburg expression is written. The large D phase is studied using...

Finite-size scaling of energies in several isotropic XY chains with defects is discussed. The finite-size corrections of ground-state and low-lying energies in the models are calculated analytically and numerically. Critical exponents of some correlation functions of the relevant models are also...

In this paper we study quantum-phase transition in the one-dimensional XY model with an XY easy-plane single ion anisotropy. We use the path-integral formalism, but consider the effect of quantum fluctuations, which renormalize the parameters of the system, using the self-consistent harmonic...

We discuss some recent determinations of the equation of state for the XY and the Heisenberg universality class.

We investigate phase transitions of XY model on a three-layer triangular lattice by assuming that the intralayer interactions on the first and the third layer are antiferromagnetic and the one on the second layer ferromagnetic. We use Monte Carlo simulations and find that there are two critical...

We investigate ground-state properties of antiferromagnetic thin films of the XY model under an external magnetic field and a uniaxial potential by numerical calculations. We clarify surface effects by comparing the ground-state properties of thin films with those of the system with infinite...

In this paper we study the quantum phase transition in a three-dimensional XY model with single-ion anisotropy D and spin S=1. The low D phase is studied using the self consistent harmonic approximation, and the large D phase using the bond operator formalism. We calculate the critical value of...

The dynamic susceptibility χQzz(ω) of the isotropic XY-model (s=12) on the alternating superlattice (closed chain) in a transverse field h is obtained exactly at arbitrary temperatures. It is determined from the results obtained for the dynamic correlations 〈Sj,nz(t)Sl,mz(0)〉, which have...