A new application of finite size scaling to Monte Carlo simulations is introduced. Using this technique, critical behavior can be investigated at temperatures arbitrarily close to the critical point without large lattice sizes. Applying this method to the two-dimensional standard 0(3) model it is shown that for the correlation length asymptotic scaling holds for /3 > 2.25; the magnetic susceptibility converges to the asymptotic scaling very slowly. In the scaling region, it is observed that the specific heat decreases with /3, which implies no singular behavior of the specific heat for this model. PACS numbers: 02.70.-c, 12.38.Gc, 64.60.-i Monte Carlo simulations have been widely used for the studies of critical phenomena.The main idea behind these methods is to measure the thermodynamic values of a certain physical quantity in the scaling region and then to fit the data to a certain scaling function. The crucial diflftculty here is that, without an exact solution of the model, the scaling region cannot be determined precisely; in other words, it is impossible to predict at what range of the temperature the data can be ideally fitted to an appropriate scaling function. To avoid this ambiguity, measurements must be done arbitrarily close to the critical point. The cost is that the size of the lattice must be extremely large to obtain proper thermodynamic data. The series expansion method has the same difficulty: it is impossible to decide how many expansion terms are needed for the proper determination of critical behavior. Because of this difficulty, often, the less singular terms are included in the leading scaling function in order to fit the data obtained at temperatures not sufficiently close to the critical point. However, this procedure usually makes the fittings highly unstable.To overcome such difficulties, various methods such as finite size scaling (FSS) and the Monte Carlo renormalization group (MCRG) method have been developed. However, it turns out that the standard usage of these methods still requires large lattice sizes [1].Our technique is based on the observation that finite size eflfects of any thermodynamic quantities on a finite lattice of linear size L depend only on L/^oo? where (^oo is the bulk (thermodynamic) correlation length. More precisely, for a typical thermodynamic quantity P,
Pooit)= fp(x{t)), Xit) ^oo (0 ' fl) where t, PL, P! and fp are the reduced temperature (T -Tc)/Tc, the value of P on a lattice of linear size L, the thermodynamic value of P, and a function depending on P, respectively. Equation (1) was initially suggested by Brezin [2], and using the analyticity property of PL (t) it was shown [3] that if P has a power critical behavior, Poo{t) ~ t"'' with p>0, from Eq. (1),follows for small values of ^, where po? Pi r • • ^^^ constants depending on P. It is obvious that Eq. (2) implies the usual FSS at i = 0, PL(t = 0) ^ L^/^, and that it implies Tc{L)-Tc --l/I/^/'", considering Eq. (2) up to the second order of t [Tc{L) is the fictitious critical point on the finite la...
