Yang-Lee edge singularities from extended activity expansions of the dimer density for bipartite lattices of dimensionality 2 <= d <= 7

TL;DR

This paper extends series expansions of dimer density on bipartite lattices across dimensions 2 to 7 to analyze Yang-Lee edge singularities, providing more accurate estimates of critical exponents and dimer constants.

Contribution

It introduces extended high-order series expansions for dimer densities on various bipartite lattices and uses these to estimate critical exponents and constants more accurately.

Findings

Estimated Yang-Lee edge exponents across dimensions 2 to 7.

Provided more precise dimer constants for different lattices.

Confirmed consistency with existing theoretical predictions.

Abstract

We have extended, in most cases through 24th order, the series expansions of the dimer density in powers of the activity in the case of bipartite ((hyper)-simple-cubic and (hyper)-body-centered-cubic) lattices of dimensionalities 2<= d <= 7. A numerical analysis of these data yields estimates of the exponents characterizing the Yang-Lee edge-singularities for lattice ferromagnetic spin-models as d varies between the lower and the upper critical dimensionalities. Our results are consistent with, but more extensive and sometimes more accurate than those obtained from the existing dimer series or from the estimates of related exponents for lattice animals, branched polymers and fluids. We mention also that it is possible to obtain estimates of the dimer constants from our series for the various lattices.