Numerical Finite-size Scaling Analysis Research Articles

Finite-size effects and scaling for the thermal QCD deconfinementphase transition within the exact color-singlet partition function

We study the finite-size effects for the thermal QCD Deconfinement Phase Transition (DPT), and use a numerical finite size scaling analysis to extract the scaling exponents characterizing its scaling behavior when approaching the thermodynamic limit. For this, we use a simple model of coexistence of hadronic gas and color-singlet Quark Gluon Plasma (QGP) phases in a finite volume. The Color-Singlet Partition Function (CSPF) of the QGP cannot be exactly calculated and is usually derived within the saddle point approximation. When we try to do calculations with such an approximate CSPF, a problem arises in the limit of small temperatures and/or volumes (VT3<<1), requiring then additional approximations if we want to carry out calculations. We propose in this work a new method for an accurate calculation of any quantity of the finite system, without explicitly calculating the CSPF itself and without any approximation. By probing the behavior of some useful thermodynamic response functions on the hole range of temperature, it turns out that in a finite size system, all singularities in the thermodynamic limit are smeared out and the transition point is shifted away. A numerical finite size scaling analysis of the obtained data allows us to determine the scaling exponents of the QCD DPT. Our results expressing the equality between their values and the space dimensionality is a consequence of the singularity characterizing a first order phase transition and agree very well with the predictions of other FSS theoretical approaches and with the results of both lattice QCD and Monte Carlo models calculations.

Low-lying excitations in the square - triangle random tiling model

We consider the sub-dominant eigenstates of the transfer matrix for the square - triangle random tiling model on an infinite strip of width L. A numerical algorithm for generation of the corresponding solution of the Bethe ansatz is developed. Numerical finite-size scaling analysis of the associated eigenvalues reveals the presence of both integer and non-integer critical exponents. The analytical value of one of the non-integer exponents is found. It is also shown numerically that, along with the leading correction to the free-energy density, for some excitations there is a term proportional to .

Roughening-induced deconstruction in (100) facets of CsCl-type crystals

The staggered six-vertex model describes the competition between surface roughening and reconstruction in (100) facets of CsCl-type crystals. Its phase diagram does not have the expected generic structure, due to the presence of a fully packed loop-gas line. We prove that the reconstruction and roughening transitions, cannot cross nor merge with this loop-gas line if these degrees of freedom interact weakly. However, our numerical finite size scaling analysis shows that the two critical lines merge along the loop-gas line, with strong-coupling scaling properties. The central charge is much larger than 1.5 and roughening takes place at a surface roughness much larger than the conventional universal value. It seems that additional fluctuations become critical simultaneously.