Related papers: On the Potts model partition function in an extern…
Character expansion developed in real space renormalization group (RSRG) approach is applied to U(1) lattice gauge theory with $\th$-term in 2 dimensions. Topological charge distribution $P(Q)$ is shown to be of Gaussian form at any…
The monopole-dimer model introduced recently is an exactly-solvable signed generalisation of the dimer model. We show that the partition function of the monopole-dimer model on a graph invariant under a fixed-point free involution is a…
Following the work by Houghton, Reeve and Wallace about an alternative formulation of the $n \to 0 $ limit of the $(n+1)$ state Potts model in field theory for the large order behaviour of the perturbative expansion, we generalise their…
In this paper, we explore the properties of zeta functions associated with infinite graphs of groups that arise as quotients of cuspidal tree-lattices, including all non-uniform arithmetic quotients of the tree of rank one Lie groups over…
There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two…
In this paper, we introduce a novel and general method for computing partition functions of solvable lattice models with free fermionic Boltzmann weights. The method is based on the ``permutation graph'' and the ``$F$-matrix'': the…
We have done a study of the zero-dimensional $\lambda\phi^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda)>0$. Secondly, an analytic continuation of…
The zeta functions for the Schr\"odinger equation with a triangular potential are investigated. Values of the zeta functions are computed using both the Weierstrass factorization theorem and analytic continuation via contour integration.…
In this work we calculate the partition functions of $\mathcal{N}=1$ type 0A and 0B JT supergravity (SJT) on 2D surfaces of arbitrary genus with multiple finite cut-off boundaries, based on the $T\bar{T}$ deformed super-Schwarzian theories.…
We develop a new closed-form arithmetic and recursive formula for the partition function and a generalization of Andrews' smallest parts (spt) function. Using the inclusion-exclusion principle, we additionally develop a formula for the…
We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…
The role of Z_N symmetry in gauge theories at finite temperatures is discussed. This symmetry is studied in terms of A_0-effective potential. We consider two- and four-dimensional models where the question on physical interpretation of…
The two-point correlation function of a Potts model on a graph $G$ may be expressed in terms of the flow polynomials of `Poissonian' random graphs derived from $G$ by replacing each edge by a Poisson-distributed number of copies of itself.…
We propose a novel fermionic model on the graphs. The Dirac operator of the model consists of deformed incidence matrices on the graph and the partition function is given by the inverse of the graph zeta function. We find that the…
We continue to investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence begun in arxiv:0708.0645. We derive the master matrix of the $(2,1)$…
We introduce the {\it growth partition function} $Z_{\Gamma,G}(t)$ associate with any cancellative infinite monoid $\Gamma$ with a finite generator system $G$. It is a power series in $t$ whose coefficients lie in integral Lie-like space…
This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of…
We provide new representations for the finite parts at the poles and the derivative at zero of the Barnes zeta function in any dimension in the general case. These representations are in the forms of series and limits. We also give an…
We study the geometry of $T\bar{T}$-deformed BTZ black hole and find it can be regarded as a quotient of hyperbolic space. We then consider the massive scalar field propagating in the $T\bar{T}$-deformed BTZ black hole background. The…
Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…