Self-Duality and Statistical Systems without Internal Energy Scaling Terms at Criticality

TL;DR

This paper demonstrates that self-duality in certain statistical systems causes the internal energy's finite-size scaling amplitude to vanish at criticality, enabling more precise critical temperature estimates.

Contribution

It introduces a new approach leveraging self-duality to improve critical temperature estimation in systems within the same universality class.

Findings

Self-duality leads to zero finite-size scaling amplitude of internal energy.

Equality of internal energies across system sizes yields accurate critical temperatures.

Numerical and analytical evidence supports the conjecture for specific lattice models.

Abstract

It is argued that self-duality of one system leads to the zero finite-size scaling amplitude of the critical internal energy for all system belonging to the same universality class. For such models, we may expect that condition of equality (up to correction-to-scaling terms) of the internal energies for systems with different sizes will yield more accurate estimates for the critical temperature than the scaling equation for the inverse correlation lengths which is used in the standard phenomenological renormalization-group approach. Analytical and numerical evidences confirming the above conjecture are given for examples of two-dimensional next-nearest-neighbour and spin-1 Ising lattices.