On ruelle's ξ-function for exponentially decreasing potentials

We show that Ruelle's generalised -function for a classical one-dimensional lattice spin system with two-body interaction (i) exp(-i )a(i) with >1 extends to a meromorphic function in the whole complex plane.     

Bounds on the correlations and analyticity properties of ferromagnetic Ising spin systems

We consider a ferromagnetic Ising spin system isomorphic to a lattice gas with attractive interactions. Using the Fortuin, Kasteleyn and Ginibre (FKG) inequalities we derive bounds on the decay of correlations between two widely separated sets of particles in terms of the decay of the pair correlation. This leads to bounds on the derivatives of various orders of the free energy with respect to the magnetic fieldh, and reciprocal temperature . In particular, if the pair correlation has an upper bound (uniform in the size of the system) which decays exponentially with distance in some neighborhood of (,h) then the thermodynamic free energy density (,h) andall the correlation functions are infinitely differentiable at (,h). We then show that when only pair interactions are present it is sufficient to obtain such a bound only ath=0 (and only in the infinite volume limit) for systems with suitable boundary conditions. This is the case in the two dimensional square lattice with nearest neighbor interactions for 0<₀, where ₀ ^–1 is the Onsager temperature at which (,h=0) has a singularity. For >₀, (,h)/h is discontinuous ath=0, i.e. ₀=_c, where _c ^–1 is the temperature below which there is spontaneous magnetization.Research supported by AFOSR Contract # F 44620-71-C-0013.     

Finite-Volume Glauber Dynamics in a Small Magnetic Field

We consider Glauber dynamics on a finite cube in d-dimensional lattice (d2), which is associated with basic Ising model at temperature T=1/1 under a magnetic field h > 0. We prove that if the effective magnetic field is positive, then the relaxation of the Glauber dynamics in the uniform norm is exponentially fast, uniformly over the size of underlying cube. The result covers the case of the free-boundary condition with arbitrarily small positive magnetic field. This paper is a continuation of an attempt initiated earlier by Schonmann and Yoshida to shed more light on the relaxation of the finite-volume Glauber dynamics when the thermodynamic parameter (, h) is so near the phase transition line, (, h); _c < &h = 0, that the Dobrushin–Shlosman mixing condition is no longer available.     

An upper bound on the critical temperature for a continuous system with short-range interaction

A classical gas with short-range interaction in the grand canonical ensemble is studied. Ifp(, z) denotes the thermodynamic pressure at inverse temperature and activityz, then it follows from the Mayer expansion thatp(, z) is infinitely differentiable provided andz are sufficiently small. Here it is shown that there exists ₀>0 such thatp(, z) is infinitely differentiable if< ₀ andz>0. One can interpret this result as saying that ( ₀)^–1 is an upper bound on the critical temperature for the system.     

Percolation of the minority spins in high-dimensional Ising models

We present some new results on the region in the-h plane where the + spins percolate for the nearest neighbor Ising model. In particular, it is shown that in high enough dimensionsd there is percolation of the minority spins at inverse temperatures< ₊ with some ₊>_c, for which ₊/gb_c1/2log(cd),c a constant.On leave from Rutgers University.     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Analytic and clustering properties of thermodynamic functions and distribution functions for classical lattice and continuum systems

Our most complete results concern the Ising spin system with purely ferromagnetic interactions in a magnetic fieldH (or the corresponding lattice gas model with fugacityz=const. exp(–2mH) wherem is the magnetic moment of each spin). We show that, in the limit of an infinite lattice, (i) the free energy per site and the distribution functionsn _s (x ₁, ...,x _s ; ,z) are analytic in the two variables andH if the reciprocal temperature >0 and the complex numberH is not a limit point of zeros of the grand partition function , and (ii) the Ursell functionsu _s (x ₁, ...,x _s ; ,z) tend to 0 as _s Max _{i, j} |x _i –x _j | if >0 and ReH0; in particular, if the interaction potential vanishes for separations exceeding some fixed cutoff value , then |u _s |<C exp [(–2 m |ReH|+) _s /] where is any small positive number andC is independent of _s . One consequence of the result (i) is that a phase transition can occur as is varied at constantH only ifH is a limit point of zeros of (which can happen only if ReH=0); this supplements Lee and Yang's result that the same condition is necessary for a phase transition whenH is varied at constant .For a lattice or continuum gas with non-negative interaction potential (corresponding, in the lattice case, to an Ising antiferromagnet), similar results are shown to hold provided >0 and the complex fugacityz is less than the radius of convergence of the Mayerz expansion; for the continuum gas, however,n _s andu _s must be replaced by their values integrated over small volumes surrounding each of the pointsx ₂, ...,x _s .It is shown that the pressurep is analytic in both andz, if it is analytic inz at fixed over a suitable range of values of andz, and further that, except for continuum systems without hard cores,p,n _s andu _s have convergent Maclaurin expansions in for small enoughz.Supported by the U.S. Air Force Office of Scientific Research under grant no. AF 68-1416.     

A cosmology without big bang

In contrast to standard ECSK theory with the Brans-Dicke scalar field () nonminimally coupled to the curvature scalar, an additional new pseudo scalar term ⁿ E R (contraction between Levi-Civita pseudo tensor and curvature tensor) has been included in the Lagrangian. The new term is non-zero due to the non-symmetric nature of the connection and vanishes identically in the general theory of relativity. We show that there exists a nonsingular cosmological solution for a spatially flat (k=0) Robertson-Walker line element in the radiation era; therefore our model has no big bang.     

Experimental investigation of the nonlinear properties of the surface helical instability in germanium

The results of an experimental investigation of the parameters of the surface helical instability (SHI) in germanium are presented. The dependence of the amplitude of the current oscillations of the helical wave and frequency on the electric E and magnetic B fields with E and B significantly exceeding the threshold values E_t and B_t are presented for the case of nonequilibrium (for temperatures T < 343°K) and equilibrium (T 343°K) plasma. It is shown that for small supercriticality (_E = (E-E_t)/Et 1, = ( -_t)/_t 1) > the square of the amplitude of the current oscillations and the frequency shift are proportional to the supercriticality, i.e., the regime for excitation of SHI is soft.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 18–21, May, 1981.     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

Between Equilibrium Fluctuations and Eulerian Scaling: Perturbation of Equilibrium for a Class of Deposition Models

We investigate propagation of perturbations of equilibrium states for a wide class of 1D interacting particle systems. The class of systems considered incorporates zero range, K-exclusion, misanthropic, bricklayers models, and much more. We do not assume attractivity of the interactions. We apply Yau's relative entropy method rather than coupling arguments. The result is partial extension of T. Seppäläinen's recent paper. For 0<<1/5 fixed, we prove that, rescaling microscopic space and time by N, respectively N ¹⁺ , the macroscopic evolution of perturbations of microscopic order N ^– of the equilibrium states is governed by Burgers' equation. The same statement should hold for 0<<1/2 as in Seppäläinen's cited paper, but our method does not seem to work for 1/5.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

Four-parametric regular black hole solution

We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments and , respectively. For 3, 4, and |q|2s _c m the corresponding solutions are regular charged black holes. For = 3, they also satisfy the weak energy condition. For = = 0 we recover the Reissner–Nordström singular solution and for = 3, = 4 the family includes a previous regular black hole reported by the authors.     

Phases of the number-theoretic spin chain

We present numerical and analytical evidence for a first-order phase transition of the ferromagnetic spin chain with partition functionZ()=(–1)/() at the inverse temperature _cr=2.     

Deviation of Upper Bounds of Critical Temperature of Two-Dimensional O(N) Spin Models

Critical temperature of the classical O(N) spin model in two dimensions is investigated. We show that no phase transition exists in the system if the inverse temperature is less than _c=_c(N), where _c(N) is a constant such that _c(N) > const. N log N.     

Symmetry properties of nonlinear barrier coefficients

This paper concerns the properties of a symmetric barrier between two reservoirs. The barrier can passK conserved quantities. The current of theith quantity is assumed to satisfy the nonlinear relationJ _i=A _ijj+B_ijkljkl where the _i's are the affinity differences across the barrier andA _ij andB _ijkl are functions of the average affinities of the reserviors. It is shown thatB _ijkl is symmetric in all indices.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

The nonlinear self-defocusing electromagnetic surface waves in a metalised ferrite film

The dispersion relations for TE s-polarized nonlinear electromagnetic surface waves guided by a metallised ferrite film, surrounded by a nonlinear self-defocusing dielectric cover with intensity dependent refractive indices have been computed. Numerical results are also illustrated to show the propagation characteristics for different values of the film thickness, and at a fixed value of the dielectric-ferrite interface nonlinearity. It has been found that the surface waves exist in both directions of propagation, where the external field is applied. The propagation of these waves is non-reciprocal, and has a resonant interaction in the reverse direction. The power flow carried by the structure has also been calculated for different values of the slab thickness. The non-reciprocity has also been obsorved, and the power flow level can been controlled by the film thickness. of semi-infinite gyromagnetic and nonlinear media². If we increase the operating frequency, the power flow level changes at a fixed film thickness, for 0 and for 0 as in Figs.4. There exist a limited eigenvalues (solutions) with f=17.8GHz for 0, and for different values of the operating frequency for 0. So the eigenvalues and the power flow level can be varied as the operating frequency is tunned. At f=17.8GHz for 0, as in fig.4b, to some value of the power flow there correspond two propagation wave index, which are being related to bistable states of nonlinear surface. All the above mentioned behaviours exhibit the characteristics of microwave switches, isolators, and limiters and could be used in some experimental applications in Microwave Engineering Technology. The other parameters effects as the magnetic field, magnetization, types of ferrite etc. on the dispersion characteristics and the power flow are now under consideration.     

Unusual Corrections to Scaling in the 3-State Potts Antiferromagnet on a Square Lattice

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2 and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as J/kT according to Ae ² (1+be ^– +···), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.