Surface Transitions of the Semi-Infinite Potts Model I: The High Bulk Temperature Regime

We propose a rigorous approach of Semi-Infinite lattice systems illustrated with the study of surface transitions of the semi-infinite Potts model.     

Phase Transitions in the Two-Dimensional Slightly Diluted Five-Vertex Potts Model

Physics of the Solid State - Phase transitions in the two-dimensional slightly diluted Potts model on a square lattice at q = 5 have been studied using the computer simulation method. The systems...     

The Riemann Surface of the Chiral Potts Model Free Energy Function

In a recent paper we derived the free energy or partition function of the N-state chiral Potts model by using the infinite lattice inversion relation method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site T _pq of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of T _pq . In terms of the t _p ,t _q variables, it consists of an infinite number of Riemann sheets, each sheet corresponding to a point on a (2N–1)-dimensional lattice (for N>2). The function T _pq is meromorphic on this surface: we obtain the orders of all the zeros and poles. For N odd, we show that these orders are determined by the usual inversion and rotation relations (without the extra symmetry), together with a simple linearity ansatz. For N even, this method does not give the orders uniquely, but leaves only [(N+4)/4] parameters to be determined.     

Monte-Carlo Calculations for the Surface on a Semi-Infinite XY Model

We study the critical behavior of the surface on a semi-infinite simple-cubic-lattice XY model by Monte-Carlo simulations. .Our results show that a distinct surface phase exists for relatively strong surface coupling above the bulk critical temperature. Moreover, we find that the surface susceptibility diverges in the whole range of the surface phase, which supports that the surface phase is a KT phase.     

Effect of Quenched Nonmagnetic Impurities on the Phase Transitions in a Three-Dimensional Potts Model

Journal of Experimental and Theoretical Physics - The influence of a weak disorder in the form of quenched nonmagnetic impurities on the phase transitions (PTs) in a three-dimensional 5-state Potts...     

Numerical Calculations for the Surface on a Semi-Infinite Ising Model with a Random Surface Field

We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormaliza tion group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface. specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large and om field.     

Complete Analyticity of the 2D Potts Model above the Critical Temperature

We investigate the complete analyticity (CA) of the two-dimensional q-state Potts model for large values of q. We are able to prove it for every temperature , provided we restrict ourselves to nice subsets, their niceness depending on the temperature T. Contrary to this restricted complete analyticity (RCA), the full CA is known to fail for some values of the temperature above . Our proof is based on Pirogov-Sinai theory and cluster expansions for the Fortuin-Kasteleyn representation, which are available for the Potts model at all temperatures, provided q is large enough. Received: 16 July 1996 / Accepted: 8 January 1997     

The Properties of Surface Polaron in the Semi-Infinite Polar Crystal

The effective Hamiltonian and the renormalized mass of surface polaron, where the electron is strongly coupled with the surface optical (SO) phonons but weakly or intermediately coupled with the bulk longit udinal-optical (LO) phonons, were first reviewed. The self-energy and the renormalized mass of the polaron for the polar crystals of potassium iodide, silver chloride and silver bromide are evaluated as a function of the depth Gom the crystal surface. Results of our calculation indicate that the effect of the electron-SO phonon interaction is dominant only within a very small layer from the crystal surface. Its justification awaits further experimental results.     

Some Considerations on the Derivation of the Nonlinear Quantum Boltzmann Equation II: The Low Density Regime

In this paper we analyse the asymptotic dynamics of a system of N identical quantum particles in a low-density regime. Our approach follows the strategy introduced by the authors in a previous work,⁽²⁾ to treat the simpler weak coupling regime. The time evolution of the Wigner transform of the one-particle reduced density matrix is represented by means of a perturbative series. The expansion is obtained upon iterating the Duhamel formula, in the spirit of the paper by Lanford.⁽³²⁾ For short times and small interaction potential, we rigorously prove that a subseries of the complete perturbative series, converges to the solution of the nonlinear Boltzmann equation that is physically relevant in the context. An important point is that we completely identify the cross-section entering the limiting Boltzmann equation, as being the Born series expansion of quantum scattering.As in ref. 2, our convergence result is only partial, in that we merely characterize the asymptotic behaviour of a subseries of the complete original perturbative expansion. We only have plausibility arguments in the direction of proving that the terms we neglect, when going from the original series to its associated subseries, are indeed vanishing in the limit.The present study holds in any dimension d ≥ 3.     

The Order Parameter of the Chiral Potts Model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ‘‘broken rapidity line’’ approach pioneered by Jimbo et al. (J. Phys. A 26:2199--2210 (1993).).     

Correlation at Low Temperature: II. Asymptotics

The present paper is a continuation of ref. 4, where the truncated two-point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature, under a weak coupling assumption. In this paper we compute the asymptotics of the correlation function as the temperature goes to zero. This paper thus extends ref. 3 in two directions: The Hamiltonian function is allowed to have several local minima other than a unique global minimum, and we do not require translation invariance of the Hamiltonian function. We are in particular able to handle spin systems on a general lattice.     

The Phase Transition in the Three-State Potts Model: An Analytical Analysis

Weinvestigate thephase transition of the three-state Potts model in an analytical approachthe generalized cumtilant expansion with the effective mean field Itypothesis. We find a first order phase transition in the three-dimensional three-state Pot ts model with ferromagnetic nearest neighbor (nn) coupling. For the model with antiferromagnetic next-to-nearest neighbor (nnn) coupling, pe find a first order transition when tlle relative strength of the nnncoupling γ is fixed to -0.2. The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.     

Low temperature properties of the random field Potts chain

The random field q-states Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case (q = 2). This is also the expected outcome based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field perturbations (`chaos') and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,..., 5. Finally for q = 2 (Ising case) the domain length distribution is studied for correlated random fields. Received 27 August 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: rieger@lusi-sb.de     

Phase Transitions in the Diluted Two-Dimensional Potts Model with the Number of Spin States q = 3 on a Square Lattice

Physics of the Solid State - The phase transitions in the two-dimensional diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems...     

Phase Transitions and the Thermodynamic Properties of the Potts Model with the Number of Spin States q = 4 on a Triangular Lattice

Physics of the Solid State - The phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a triangular lattice are...     

低喷淋密度超亲水表面水平管降液膜温度分布

水平管降液膜蒸发广泛应用在石油、化工、海水淡化等领域,对低喷淋密度温度演化规律的研究有助于拓宽其应用范围,理解其微观机理。本文在超亲水表面上结合红外热追踪技术,对水平管降液膜表面的温度演化规律进行了研究,分析了温度分区现象和温升规律。实验中首次发现了马鞍形液膜内部的高温环状结构,并结合三维数值模拟揭示了掺混作用导致的局部高温环状结构形成的内部机理。     

Series Analysis of a Kosterlitz-Thouless Transition: The 6-State Planar Potts Model

A new implementation of the Finite Lattice Method of series expansion is used to derive low temperature series for the 6-state planar Potts model. This is expected to have Kosterlitz-Thouless transitions between the ordered low-temperature phase and a massless phase, and between the massless phase and a high-temperature disordered phase. In an exploratory study, we have analysed series for the order parameter to order x ⁵⁹. These series have proved particularly difficult to analyse and when seeking to both locate the transition and confirm the form of the Kosterlitz-Thouless transition, considerable ambiguity is found. If however the form of the Kosterlitz-Thouless transition is assumed, then the series analysis consistently indicates that the lower transition occurs at x _L=0.4886(10). A more conservative analysis, which made no assumption about the nature of the transition, led to the estimate x _L=0.485(8).     

The Theory of the Low Pressure Discharge in the Strong Ionization Regime

A system of integro-differential equations describing the velocity distribution functions of the neutral atoms and of the ions and the radial profiles of the electric potential and the particle densities in the positive column at low pressures and high degrees of ionization is derived. This system is solved for a simplified, but self-consistent, plane model. Both the initial velocity of the ions and the neutral gas depletion caused by the ionization processes are taken into account. For a cylindrical model a solution is obtained for the region near the axis. With rising neutral gas temperature the radial ion flux density is slightly increasing. The pressure tensor, the heat flux tensor, and several components of the corresponding tensor of the fourth order for the ion gas are calculated. It is shown that on the axis the radial and the azimuthal ion temperatures are smaller than the neutral gas temperature because the ions generated out of neutral atoms are retarded during the flight to the axis.