Brown, RG; Ciftan, M, *Critical behavior of the helicity modulus for the classical Heisenberg model*,
Physical Review B, vol. 74 no. 22
(Winter, 2006) [doi] .
**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 nonzero topological charge, establishing a connection between topological charge and helicity in the model. © 2006 The American Physical Society.*