Ralph Kenna

The Strength of First and Second Order Phase Transitions from Partition Function Zeroes

We present a numerical technique employing the density of partition function zeroes (i) to distinguish between phase transitions of first and higher order, (ii) to examine the crossover between such phase transitions and (iii) to measure the strength of first and second order phase transitions in the form of latent heat and critical exponents. These techniques are demonstrated in applications to a number of models for which zeroes are available.

Finite-size scaling and corrections in the Ising model with Brascamp-Kunz boundary conditions

The Ising model in two dimensions with the special boundary conditions of Brascamp and Kunz is analyzed. Leading and subdominant scaling behavior of the Fisher zeros are determined exactly. The exact finite-size scaling, with corrections, of the specific heat is determined both at critical and effective critical (pseudocritical) points. The shift exponents associated with the scaling of these effective critical points are not the same as the inverse correlation length critical exponent. All corrections to scaling are analytic.

Phase transition strengths from the density of partition function zeroes

Abstract We report on a new method to extract thermodynamic properties from the density of partition function zeroes on finite lattices. This allows direct determination of the order and strength of phase transitions numerically. Furthermore, it enables efficient distinguishing between first- and second-order transitions, elucidates crossover between them and illuminates the origins of finite-size scaling. The power of the method is illustrated in typical applications for both Fisher and Lee-Yang zeroes.

Critical behavior of the two-dimensional step model

We use finite--size scaling of Lee--Yang partition function zeroes to study the critical behaviour of the two dimensional step or sgn

Density of partition function zeroes and phase transition strength

O(2)

The structure of the Aoki phase at weak coupling

model. We present evidence that, like the closely related

Weakly coupled Gross-Neveu model with Wilson fermions

XY

Analysis of the Density of Partition Function Zeroes: A Measure for Phase Transition Strength

--model, this has a phase transition from a disordered high temperature phase to a low temperature massless phase where the model remains critical. The critical parameters (including logarithmic corrections) are compatible with those of the

Exact finite-size scaling with corrections in the two-dimensional Ising model with special boundary conditions

XY

The phase diagrams of the schwinger and gross-neveu models with Wilson fermions

--model indicating that both models belong to the same universality class.