We introduce a natural nonhierarchical version of Derrida's generalized random energy model. We prove that, in the thermodynamical limit, the free energy is the same as that of a suitably constructed GREM. The Annals of Applied Probability 2006, Vol. 16, No. 1, 1–14 DOI: 10.1214/105051605000000665 © Institute of Mathematical Statistics, 2006 ON A NONHIERARCHICAL VERSION OF THE GENERALIZED RANDO...

We consider the thermodynamics of minimally coupled massive scalar field in 3+1 dimensional Taub-NUT background. The brick wall model of 't Hooft is used. When Schwarzschild like coordinates are used it is found that the usual radial brick wall cutoff parameter is required to regularize the solution. Free energy of the scalar field is obtained through explicit counting of states. It is found th...

In his recent paper [6] Michel Talagrand gave a rigorous proof of the Parisi formula for the free energy of the Sherrington-Kirkpatrick model. In the present paper we utilize the methodology developed in [6] to compute the thermodynamic limit of the free energy of the set of configurations with the fixed average of spins N−1 ∑ i≤N σi = uN as uN → u ∈ [−1, 1].

It is known that non-holomoorphic corrections are necessary in order to get duality invariant free energy and entropy function. However the present methods of incorporating non-holomorphic corrections are in conflict with special geometry properties of moduli space. The moduli fields do not transform in duality covariant way and their duality transformation also involves the graviphoton field s...

A mean field spin system consisting two interacting groups each with homogeneous interaction coefficients is introduced and studied. Existence of the thermodynamic limit is shown by an asymptotic sub-addittivity method and factorization of correlation functions is proved almost everywhere. The free energy solution of the model is obtained by upper and lower bounds and by showing that their diff...

We derive the moduli dependence of the one–loop gauge couplings for non– vanishing gauge background fields in a four–dimensional heterotic (0,2) string com-pactification. Remarkably, these functions turn out to have a representation as modular functions on an auxiliary Riemann surface on appropriate truncations of the full moduli space. In particular, a certain kind of one–loop functions is giv...

High derivative terms do not play a major role in field theories because of the associated complexity and inherent difficulty in connecting these terms to physically measurable quantities. A role for higher derivative terms is analyzed for the case of field theories used to describe phase separated systems. In these theories, higher derivative terms are directly connected to an interfacial free...

Using the standard saddle-point method, we find an explicit relation for the large-N limit of the free energy of an arbitrary generalized 2D Yang-Mills theory in the weak (A < Ac) region. In the strong (A > Ac) region, we investigate carefully the specific fourth Casimir theory, and show that the ordinary integral equation of the density function is not adequate to find the solution. There exis...