Critical behavior of the helicity modulus for the classical Heisenberg model

The critical scaling of the helicity modulus of the classical O(3) 3d Heisenberg ferromagnet is studied directly. Monte Carlo methods that impose either an antiperiodic boundary condition or a finite twist of definite handedness across otherwise periodic boundaries in one lattice direction are used to measure scale-dependent enthalpy variations in a simple cubic lattice at the ferromagnetic critical temperature. Finite-size scaling is then used to determine the critical exponents vE and vF for helicity and, by evaluating three independent hyperscaling-linked pairs of ν and α, to test hyperscaling for this model. It is observed that antiperiodic boundary conditions in particular constrain the lattice to have a nonzero topological charge, establishing a connection between topological charge and helicity in the model. © 2006 The American Physical Society.

Duke Scholars

Author Robert Brown Physics