Renormalization group analysis of finite-size scaling in the ø44 model

Abstract

A finite-size scaling theory for the φ 4 4 model is derived using renormalization group methods. Particular attention is paid to the partition function zeroes, in terms of which all thermodynamic observables can be expressed. While the leading scaling behaviour is identical to that of mean field theory, there exist multiplicative logarithmic corrections too. A non-perturbative test of these formulae in the form of a high precision Monte Carlo analysis reveals good quantitative agreement with the analytical predictions. * Supported by Fonds zur Förderung der Wissenschaftlichen Forschung inÖsterreich, project P7849.

Scaling and density of Lee-Yang zeros in the four-dimensional Ising model

“…At d = 4 the mean field powerlaw scaling behaviour is modified by multiplicative logarithmic correctionsa circumstance intimately related to the expected triviality of the theory [14,15,16]. Logarithmic corrections to the finite-size scaling of partition function zeroes in four dimensions have recently been identified from a perturbative renormalization group analysis backed up by a high precision numerical study [17].…”

“…One has to rely on finite-size scaling (FSS) extrapolation methods to gain information on the corresponding thermodynamic limit. Let P L (t) represent the value of some thermodynamic quantity P at reduced temperature t on a lattice characterized by a linear extent L. Then, if ξ is the correlation length, the FSS hypothesis is that [17,27] …”

“…The perturbative RG analysis of the finite-size φ 4 4 model [17] gives the relationship between the magnetization M L (t, H) and external field H at reduced temperature t…”

“…We now compare these FSS results with data obtained for the 4D Ising model in a high statistics Monte Carlo calculation. The simulation was done with the Swendsen-Wang cluster updating algorithm [7] applied to lattices of sizes L 4 for lattice sizes with linear extension L = 8, 12, 16, 20, 24 (details of the numerics can be found in [17]). …”

Excitation-Gap Scaling near Quantum Critical Three-Dimensional Antiferromagnets

“…Due to a logarithmic decay of the renormalized interaction strength upon approaching the critical point, this field theory exhibits logarithmic corrections to a Gaussian fixed point [7][8][9][10]. This leads to characteristic multiplicative logarithmic scaling corrections to the bare mean-field behavior in various physical quantities that are in principle accessible by several experimental probes, such as in thermodynamic measurements or neutron and light scattering techniques [6,[11][12][13][14], if probed at the relevant energy scales near the quantum critical point.…”