The Fukui-Todo algorithm is an important element of the array simulational approaches to tackling critical phenomena in statistical physics. partition-function-zero approach fundamental importance understanding such and a precise tool measure their properties. However, because bypasses sample-by-sample energy computation, zeros cannot easily be harnessed through distribution. Here this obstacle...

We study topological defect lines in two character rational conformal field theories. Among them one set of theories are commutant pairs $E_{8,1}$ theory. Using these we construct partition function the $E_8$ find that defects preserve only a part current algebra symmetry. also determine $c=24$ CFTs using 2 and that, with appropriate choice pairs, all symmetries c = 24 CFTs.

A vertex|matching-partition (V |M) of a simple graph G is a spanning collection of vertices and independent edges of G. Let vertex v ∈ V have weight wv and edge e ∈ M have weight we. Then the weight of V |M is w(V |M) = ∏ v∈V wv · ∏ e∈M we. Define the vertex|matching-partition function of G as W(G) = ∑ V |M w(V |M). In this paper we study this function when G is a path and a cycle. We generate ...

We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must ...

A new recursive procedure of the calculation of a restricted partition function is suggested. An explicit combinatorial formula for the restricted partition function is found based on this procedure.

We obtain large N asymptotics for the random matrix partition function