The X-Y model in one- and two-dimensions is investigated by means of the path integral. The low temperature properties are shown to be described by the phase mode. In particu-lar, the quantum model in the limit S--'fco is found to be well expressed by the planer model. The spin-correlation functions are calculated explicitly. As a result it is found that at zero temperature the quasi long-range order in one-dimension and the long-range order in two-dimen-sions appear. The spontaneous magnetization is explicitly given at zero temperature in two-dimensions. At finite temperatures the dynamical behaviour is the same as that studied by Nelson and Fisher. The divergence of the susceptibility at T=O in one-dimension is shown to be different from that of the classical model. Considerable progress has been made recently 111 understanding the nature of the phase transition in the two-dimensional planer model without long-range or-cler.l)~81 It has been revealed that below the transition temperature there exists a topological order in which bound pairs of vortex and antivortex are formed, theThe X-Y model in one- and two-dimensions is investigated by means of the path integral. The low temperature properties are shown to be described by the phase mode. In particu-lar, the quantum model in the limit S--'fco is found to be well expressed by the planer model. The spin-correlation functions are calculated explicitly. As a result it is found that at zero temperature the quasi long-range order in one-dimension and the long-range order in two-dimen-sions appear. The spontaneous magnetization is explicitly given at zero temperature in two-dimensions. At finite temperatures the dynamical behaviour is the same as that studied by Nelson and Fisher. The divergence of the susceptibility at T=O in one-dimension is shown to be different from that of the classical model. Considerable progress has been made recently 111 understanding the nature of the phase transition in the two-dimensional planer model without long-range or-cler.l)~81 It has been revealed that below the transition temperature there exists a topological order in which bound pairs of vortex and antivortex are formed, the

Progress of Theoretical PhysicsApr 1, 19806 citations

Short and long distance behaviour of two point correlation functions in integrable coupled minimal models

Pascal Baseilhac

Using the exact result for the vacuum expectation values in non-simply laced affine Toda field theory $C_2^{(1)}$ , we study short and long distance predictions of the two-point correlation functions in the massive phase of two coupled minimal models. The central charge of the unperturbed models ranges from $c=1$ to $c=2$ , where the perturbed models correspond to two magnetically coupled Ising models and Heisenberg spin ladders, respectively.Using the exact result for the vacuum expectation values in non-simply laced affine Toda field theory $C_2^{(1)}$, we study short and long distance predictions of the two-point correlation functions in the massive phase of two coupled minimal models. The central charge of the unperturbed models ranges from $c=1$ to $c=2$, where the perturbed models correspond to two magnetically coupled Ising models and Heisenberg spin ladders, respectively.

May 17, 20000 citations

Integrable spin- particle systems with long-range interactions

Kazuhiro Hikami, Miki Wadati

Physics Letters AFeb 1, 199347 citations

Long-time asymptotics of the long-range Emch-Radin model

Michael Kästner

Abstract The long-time asymptotic behaviour is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behaviour. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration.Abstract The long-time asymptotic behaviour is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behaviour. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration.

Open PhysicsJan 1, 201215 citations

Using the exact result for the vacuum expectation values in non-simply laced affine Toda field theory

C_2^{(1)}

, we study short and long distance predictions of the two-point correlation functions in the massive phase of two coupled minimal models. The central charge of the unperturbed models ranges from

c=1

c=2

, where the perturbed models correspond to two magnetically coupled Ising models and Heisenberg spin ladders, respectively.