Abstract:
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 non-zero topological charge, establishing a new connection between
topological charge and helicity in the model.