Spin and Gauge Systems on Spherical Lattices

Abstract

We present results for 2D and 4D systems on lattices with topology homotopic to the surface of a (hyper) sphere $S^2$ or $S^4$. Finite size scaling is studied in situations with phase transitions of first and second order type. The Ising and Potts models exhibit the expected behaviour; for the 4D pure gauge $U(1)$ theory we find consistent scaling indicative of a second order phase transition with critical exponent $\nu \simeq 0.36(1)$.

4 pages, LaTeX, 3 POSTSCRIPT figures (uuencoded)

References in corpus (5)

• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group
• The First Order Signal in Pure U(1) Gauge Theory May be Fake
• First-Order Signals in Compact QED with Monopole Suppressed Boundaries
• Evidence for a Critical Behavior in $4D$ Pure Compact QED

Cited by in corpus (3)

• Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory on the lattice
• Universality of the Ising Model on Sphere-like Lattices
• Critical behavior and monopole density in U(1) lattice gauge theory