The two physical parameters needed to specify the long-wavelength properties of a spin-& quantum antiferromagnet are determined numerically. The fluctuation-induced renormalization of the stiffness constant differs by 40% from the expansion results of Oguchi, necessitating a corresponding adjustment in the value of the exchange deduced from the measured correlation length. It has been established numerically'and by other means that the two-dimensional spin--, ' Heisenberg antiferromagnet on a square lattice has a conventionally ordered ground state. The staggered magnetization 0 is in fact 60% of its classical value. 'The long-range order, together with the probable absence of any topological term, makes the nonlinear cr model (NLo) a highly plausible representation of the antiferromagnet.There are then two nontrivial parameters to be determined which completely 6x the long-wavelength properties of the model and allow comparison with experiment, namely the uniform field susceptibility g and the stiffness constant p. Their bare values enter the NLo model as 2 + -, ' pp(vn) 4 2' for the smaller scales but serves to smoothly cut off the large wave numbers in the sum over the Brillouin zone which do not contribute to the leading L dependence anyway. Our data, determined by the von Neumann-Ulam method of Ref. 2, are given in Table I and plotted in Figs. 1 and 2. Our units are defined by P Heis -J Q St" SJ, (ij &where the sum runs over all nearest-neighbors pairs of sites (ij ) and the S; are Pauli matrices. For the quantum numbers S in (2) we use physical units, i.e. , S can assume any integer value~L /2. To present our results in a convention free manner, we divide out the spin-wave values of where Q is normalized to Q 1 and m is the magnetization density.We noted in a previous publication that knowledge of the Heisenberg ground-state energy as a function of lattice size (L by L sites, L even) and the total spin S suffices to determine g and p by the following asymptotic formula for the energy per site: -2.65 -2.70-1.437c, S(S+1) L3 2XL4 (2) -2.80where the spin-wave velocity c, p/g.To make the various terms plausible, we note that S should appear as S($+1) on quantum mechanical grounds and the factors of L in the last term give the proper limit for L large, S/L small but nonzero. The dominant finite-size effects involve the renormalized spin-wave velocity since it is only the long-wavelength modes that sense the presence of boundaries. The numerical coefficient, 1.437, is universal and was found by linearizing the Heisenberg Hamiltonian and computing the spin-wave energy exactly on a series of L XL lattices. The linearization is not quantitatively valid -2.85 10 15 (1 0/L)3 FIG. 1. Ground-state energy, S 0, per site vs (10/L) in units of J. The solid line has a slope of -8.85x10 and an intercept of -2.669~0.0011 (statistical error only). To assess systematic errors we show a fit (dashed hne) omitting the 4&4 point which gave an intercept of -2.665~0.002 and a slope of -1.03 x ].0 40 11 328

No abstract

No abstract

Using Monte Carlo techniques, we study the magnetic susceptibility and specific heat of the two-dimensional step model. Contrary to some theoretical expectations and numerical results, the finite-size-scale analysis of the susceptibility sho~s evidence for a possible low-temperature phase with in6nite correlation lengths and with a nondivergent speci6c heat. The absence in this model of long-lived metastable states is also analyzed.

No abstract