Grand-Canonical Ensemble of Random Surfaces with Four Species of Ising Spins

The grand-canonical ensemble of dynamically triangulated surfaces coupled to four species of Ising spins (c=2) is simulated on a computer. The effective string susceptibility exponent for lattices with up to 1000 vertices is found to be $\gamma = - 0.195(58)$. A specific scenario for $c > 1$ models is conjectured.Comment: LaTeX, 11 pages + 1 postscript figure appended, preprint LPTHE-Orsay 94/1

On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity

We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical simulation we find that the number of such triangulations containing $V$ simplices grows faster than exponentially with $V$. This property ensures that the model has no thermodynamic limit.Comment: 8 pages, 2 figure

Ising-link Quantum Gravity

We define a simplified version of Regge quantum gravity where the link lengths can take on only two possible values, both always compatible with the triangle inequalities. This is therefore equivalent to a model of Ising spins living on the links of a regular lattice with somewhat complicated, yet local interactions. The measure corresponds to the natural sum over all 2^links configurations, and numerical simulations can be efficiently implemented by means of look-up tables. In three dimensions we find a peak in the ``curvature susceptibility'' which grows with increasing system size. However, the value of the corresponding critical exponent as well as the behavior of the curvature at the transition differ from that found by Hamber and Williams for the Regge theory with continuously varying link lengths.Comment: 11 page

Generalized Penner models to all genera

We give a complete description of the genus expansion of the one-cut solution to the generalized Penner model. The solution is presented in a form which allows us in a very straightforward manner to localize critical points and to investigate the scaling behaviour of the model in the vicinity of these points. We carry out an analysis of the critical behaviour to all genera addressing all types of multi-critical points. In certain regions of the coupling constant space the model must be defined via analytical continuation. We show in detail how this works for the Penner model. Using analytical continuation it is possible to reach the fermionic 1-matrix model. We show that the critical points of the fermionic 1-matrix model can be indexed by an integer, $m$, as it was the case for the ordinary hermitian 1-matrix model. Furthermore the $m$'th multi-critical fermionic model has to all genera the same value of $\gamma_{str}$ as the $m$'th multi-critical hermitian model. However, the coefficients of the topological expansion need not be the same in the two cases. We show explicitly how it is possible with a fermionic matrix model to reach a $m=2$ multi-critical point for which the topological expansion has alternating signs, but otherwise coincides with the usual Painlev\'{e} expansion.Comment: 27 pages, PostScrip

Universal correlations for deterministic plus random Hamiltonians

We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential $\varphi$. Remarkably, this correlation function may be explicitly determined in the limit of large matrices, for any unperturbed H0 and for a class of probability distribution P$(\varphi)$ of the random potential. We find a compact representation of the correlation function. From this representation one obtains readily the short distance behavior, which has been conjectured in various contexts to be universal. Indeed we find that it is totally independent of both H0 and P($\varphi$).Comment: 26P, (+5 figures not included

On the stability of renormalizable expansions in three-dimensional gravity

Preliminary investigations are made for the stability of the $1/N$ expansion in three-dimensional gravity coupled to various matter fields, which are power-counting renormalizable. For unitary matters, a tachyonic pole appears in the spin-2 part of the leading graviton propagator, which implies the unstable flat space-time, unless the higher-derivative terms are introduced. As another possibility to avoid this spin-2 tachyon, we propose Einstein gravity coupled to non-unitary matters. It turns out that a tachyon appears in the spin-0 or -1 part for any linear gauges in this case, but it can be removed if non-minimally coupled scalars are included. We suggest an interesting model which may be stable and possess an ultraviolet fixed point.Comment: 32 pages. (A further discussion to avoid tachyons is included. To be Published in Physical Review D.

Dirac and Weyl Equations on a Lattice as Quantum Cellular Automata

A discretized time evolution of the wave function for a Dirac particle on a cubic lattice is represented by a very simple quantum cellular automaton. In each evolution step the updated value of the wave function at a given site depends only on the values at the nearest sites, the evolution is unitary and preserves chiral symmetry. Moreover, it is shown that the relationship between Dirac particles and cellular automata operating on two component objects on a lattice is indeed very close. Every local and unitary automaton on a cubic lattice, under some natural assumptions, leads in the continuum limit to the Weyl equation. The sum over histories is evaluated and its connection with path integrals and theories of fermions on a lattice is outlined.Comment: 6, RevTe

Baryon Asymmetry of the Universe in the Standard Model

We study the interactions of quarks and antiquarks with the changing Higgs field during the electroweak phase transition, including quantum mechanical and some thermal effects, with the only source of CP violation being the known CKM phase. The magnitude and sign of the predicted BAU agrees with the observed value, with moderately optimistic assumptions about the dynamics of the phase transition. At present uncertainties related to the dynamics of the ew phase transition and the oversimplifications of our treatment are too great to decide whether or not this is the correct explanation for the presence of remnant matter in our universe, however the present work makes it clear that the minimal standard model cannot be discounted as a contender for explaining this phenomenon.Comment: 121pp plus 14 figures, CERN-TH.6734/93 and RU-93-11. latex. This is an extended version of the preprint originally issued in May, 1993. It corrects some typographical errors and has been somewhat reorganized (e.g., moving more to the appendices) and elaborated (especially the section on analytic results) in order to make it more readily understandable. In addition we include two effects which were previously neglected: $L-R$ mixing due to QCD sphalerons, and a diminution of the electroweak gauge and Higgs effects in the broken phase due to mass corrections in the 1-loop approximation to th