Coordinate Deletion of Zeroes

Bessel Function Zeroes

0  1  2  3   as does its derivative  0 (): 0  0 1   0 2   0 3     0 0 = 0 01   0 02   0 03   0 04    = 0 See Tables 1 & 2 for the cases  = 0 1 2 and Tables 3 & 4 for the cases  = 12 32 52. These appear in many physical applications that we cannot hope to survey in entirety. We will state only a few properties and several importan...

Computing zeroes of spline functions

Fat Fisher Zeroes

We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (“fat”) φ random graphs and their dual quadrangulations by matching up the real part of the high and low temperature branches of the expression for the free energy. The form of this expression for the free energy also means that series expansion results for the zeroes may...

Zeroes of the Jones polynomial

We study the distribution of zeroes of the Jones polynomial VK (t) for a knot K . We have computed numerically the roots of the Jones polynomial for all prime knots with N 6 10 crossings, and found the zeroes scattered about the unit circle |t|=1 with the average distance to the circle approaching a nonzero value as N increases. For torus knots of the type (m; n) we show that all zeroes lie on ...

Thin Fisher Zeroes

Biskup et al. [Phys. Rev. Lett. 84 (2000) 4794] have recently suggested that the loci of partition function zeroes can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeroes for Ising and Potts models on non-planar (“thin”) regular random graphs using this approach, and note that the locus of Fisher zeroes on a Bethe lattice is identic...