Series expansions without diagrams

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.Comment: 24 pages, IASSNS-HEP-93/1

Specific Heat Exponent for the 3-d Ising Model from a 24-th Order High Temperature Series

We compute high temperature expansions of the 3-d Ising model using a recursive transfer-matrix algorithm and extend the expansion of the free energy to 24th order. Using ID-Pade and ratio methods, we extract the critical exponent of the specific heat to be alpha=0.104(4).Comment: 10 pages, LaTeX with 5 eps-figures using epsf.sty, IASSNS-93/83 and WUB-93-4

Large Nc Continuum Reduction and the Thermodynamics of QCD

It is noted that if large Nc continuum reduction applies to an observable, then that observable is independent of temperature for all temperatures below some critical value. This fact, plus the fact that mesons and glueballs are weakly interacting at large Nc is used as the basis for a derivation of large Nc continuum reduction for the chiral condensate. The structure of this derivation is quite general and can be extended to a wide class of observables

Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the χ2\chi^2-method

We determine the critical point and the ratios $\beta/\nu$ and $\gamma/\nu$ of critical exponents of the deconfinement transition in $SU(2)$ gauge theory by applying the $\chi^2$-method to Monte Carlo data of the modulus and the square of the Polyakov loop. With the same technique we find from the Binder cumulant $g_r$ its universal value at the critical point in the thermodynamical limit to $-1.403(16)$ and for the next-to-leading exponent $\omega=1\pm0.1$. From the derivatives of the Polyakov loop dependent quantities we estimate then $1/\nu$. The result from the derivative of $g_r$ is $1/\nu=0.63\pm0.01$, in complete agreement with that of the $3d$ Ising model.Comment: 11 pages, 3 Postscript figures, uses Plain Te

Low temperature expansion for the 3-d Ising Model

We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767

New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions

We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letter

Breakdown of large-N quenched reduction in SU(N) lattice gauge theories

We study the validity of the large-N equivalence between four-dimensional SU(N) lattice gauge theory and its momentum quenched version--the Quenched Eguchi-Kawai (QEK) model. We find that the assumptions needed for the proofs of equivalence do not automatically follow from the quenching prescription. We use weak-coupling arguments to show that large-N equivalence is in fact likely to break down in the QEK model, and that this is due to dynamically generated correlations between different Euclidean components of the gauge fields. We then use Monte-Carlo simulations at intermediate couplings with 20 <= N <= 200 to provide strong evidence for the presence of these correlations and for the consequent breakdown of reduction. This evidence includes a large discrepancy between the transition coupling of the "bulk" transition in lattice gauge theories and the coupling at which the QEK model goes through a strongly first-order transition. To accurately measure this discrepancy we adapt the recently introduced Wang-Landau algorithm to gauge theories.Comment: 51 pages, 16 figures, Published verion. Historical inaccuracies in the review of the quenched Eguchi-Kawai model are corrected, discussion on reduction at strong-coupling added, references updated, typos corrected. No changes to results or conclusion

A Noisy Monte Carlo Algorithm

We propose a Monte Carlo algorithm to promote Kennedy and Kuti's linear accept/reject algorithm which accommodates unbiased stochastic estimates of the probability to an exact one. This is achieved by adopting the Metropolis accept/reject steps for both the dynamical and noise configurations. We test it on the five state model and obtain desirable results even for the case with large noise. We also discuss its application to lattice QCD with stochastically estimated fermion determinants.Comment: 10 pages, 1 tabl

Towards a Dynamical Solution of the Strong CP Problem

It is argued that QCD might solve the strong CP problem on its own. To test this idea, a lattice simulation suggests itself. In view of the difficulty of such a calculation we have, as a first step, investigated the problem in the $CP^3$ model. The $CP^3$ model is in many respects similar to QCD. In this talk I shall present some first results of our calculation. Among other things it is shown that the model has a first order deconfining phase transition in $\theta$ and that the critical value of $\theta$ decreases towards zero as $\beta$ is taken to infinity. This suggests that $\theta$ is tuned to zero in the continuum limit.Comment: 8 pages, postscript file, DESY 94-031, HLRZ 94-13, talk given at the Third KEK Topical Conference on CP Violatio