Related papers: Exact Potts Model Partition Functions on Ladder Gr…
Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result…
In this paper we consider the algorithmic problem of sampling from the Potts model and computing its partition function at low temperatures. Instead of directly working with spin configurations, we consider the equivalent problem of…
We present a natural multiplicative theory of integer partitions (which are usually considered in terms of addition), and find many theorems of classical number theory arise as particular cases of extremely general combinatorial structure…
We study the exact statistical mechanics of Lam\'e solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schr\"odinger equation with the periodic Lam\'e potential. Since the…
The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed…
We explore systems with a large number of fermionic degrees of freedom subject to non-local interactions. We study both vector and matrix-like models with quartic interactions. The exact thermal partition function is expressed in terms of…
In his famous 2007 paper on three dimensional quantum gravity, Witten defined candidates for the partition functions $$Z_k(q)=\sum_{n=-k}^{\infty}w_k(n)q^n$$ of potential extremal CFTs with central charges of the form $c=24k$. Although such…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores…
We write exact equations for the thermodynamic properties of a linear polymer molecule confined to walk on a lattice of finite size. The dimension of the space in which the lattice resides can be arbitrary. We also calculate polymer…
We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union- Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature…
We discuss generalized partition function of 2d CFTs decorated by higher qKdV charges on thermal cylinder. We propose that in the large central charge limit qKdV charges factorize such that generalized partition function can be rewritten in…
In this paper, we study asymptotics of the thermal partition function of a model of quantum mechanical fermions with matrix-like index structure and quartic interactions. This partition function is given explicitly by a Wronskian of the…
We present exact calculations of the zero-temperature partition function, $Z(G,q,T=0)$, and ground-state degeneracy (per site), $W({G},q)$, for the $q$-state Potts antiferromagnet on a number of families of graphs ${G}$ for which the…
We present a new finite-temperature quantum Monte Carlo algorithm to compute imaginary-time Green functions for a single hole in the t-J model on non-frustrated lattices. Spectral functions are then obtained with the Maximum Entropy method.…
In some cases, an important example being at finite temperature, extreme infrared, collinear, or light-cone behaviour may cause the usual loop expansion to break down. For some of these cases higher order ladder graphs can become important.…
Based on a technique of Barvinok and Barvinok and Sober\'on we identify a class of edge-coloring models whose partition functions do not evaluate to zero on bounded degree graphs. Subsequently we give a quasi-polynomial time approximation…
We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean $AdS_2$ background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the…
In this letter we calculate the exact partition function for free bosons on the plane with lacunae. First the partition function for a plane with two spherical holes is calculated by matching exactly for the infinite set of Wilson…
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic…