Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

graham higman has defined coset diagrams for psl(2,ℤ). these diagrams are composed of fragments, and the fragments are further composed of two or more circuits. q. mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

We use Monte Carlo simulations to study chains of Isingand XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, wh...

In this paper we find all solutions of four kinds of the Diophantine equations begin{equation*} ~x^{2}pm V_{t}xy-y^{2}pm x=0text{ and}~x^{2}pm V_{t}xy-y^{2}pm y=0, end{equation*}% for an odd number $t$, and, begin{equation*} ~x^{2}pm V_{t}xy+y^{2}-x=0text{ and}text{ }x^{2}pm V_{t}xy+y^{2}-y=0, end{equation*}% for an even number $t$, where $V_{n}$ is a generalized Lucas number. This pape...

We have studied the magnetic and thermodynamic properties as well as the NMR spectra of the quasi two-dimensional Heisenberg antiferromagnet RbFe(MoO4)2. The observed temperature dependence of the order parameter, the critical indices and the overall magnetic H − T phase diagram are all in a good agreement with the theoretical predictions for a 2D XY model. The temperature dependence of the spe...

We have studied the magnetic and thermodynamic properties as well as the NMR spectra of the quasi two-dimensional Heisenberg antiferromagnet RbFe(MoO4)2. The observed temperature dependence of the order parameter, the critical indices and the overall magnetic H − T phase diagram are all in a good agreement with the theoretical predictions for a 2D XY model. The temperature dependence of the spe...

We study theNernst effect influctuating superconductors by calculating the transport coefficient xy a in a phenomenologicalmodel where the relative importance of phase and amplitude fluctuations of the order parameter is tuned continuously to smoothly evolve from an effectiveXYmodel to themore conventional Ginzburg–Landau description. To connect with a concrete experimental realizationwe choose...

B − T phase diagram and phase transitions of interlayer Josephson vortices are investigated. For magnetic fields above Bmc = φ0/2 √ 3γd, we find a Kosterlitz-Thouless (KT) type intermediate phase characterized by in-plane two-dimensional, quasi long-range orders (QLROs) of vortex alignment and superconductivity. The transformation to high-temperature normal phase is a KT transition. The evoluti...

The 3D XY model with random in-plane couplings is simulated to model the phase diagram of a disordered type II superconductor as a function of temperature T and randomness strength p for fixed applied magnetic field. As p increases to a critical p(c), the first order vortex lattice melting line turns parallel to the T axis, continuing down to low temperatures, rather than ending at a critical p...

A mean-field theory for the ordering of hydrogen molecules on a triangular net is derived in terms of the quadrupole coupling constant Γ, the crystal field Vc, and the temperature T. The phase diagram consists of six regions, separated by firstand second-order transitions. For almost all values of Vc/Γ for which ordering occurs, the disordered to ordered phase transition is continuous. At T=0 K...