The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction

This is the completion of an exploratory study of Compact lattice Quantum Electrodynamics with a weak four-fermi interaction and four species of massless fermions. In this formulation of Quantum Electrodynamics massless fermions can be simulated directly and Finite Size Scaling analyses can be performed at the theory's chiral symmetry breaking critical point. High statistics simulations on lattices ranging from $8^4$ to $24^4$ yield the equation of state, critical indices, scaling functions and cumulants. The measurements are well fit with the orthodox hypothesis that the theory is logarithmically trivial and its continuum limit suffers from Landau's zero charge problem.Comment: 27 pages, 15 figues and 10 table

Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model

The scaling behaviour of the edge of the Lee--Yang zeroes in the four dimensional Ising model is analyzed. This model is believed to belong to the same universality class as the $\phi^4_4$ model which plays a central role in relativistic quantum field theory. While in the thermodynamic limit the scaling of the Yang--Lee edge is not modified by multiplicative logarithmic corrections, such corrections are manifest in the corresponding finite--size formulae. The asymptotic form for the density of zeroes which recovers the scaling behaviour of the susceptibility and the specific heat in the thermodynamic limit is found to exhibit logarithmic corrections too. The density of zeroes for a finite--size system is examined both analytically and numerically.Comment: 17 pages (4 figures), LaTeX + POSTSCRIPT-file, preprint UNIGRAZ-UTP 20-11-9

Scaling behavior of the Heisenberg model in three dimensions

We report on extensive numerical simulations of the three-dimensional Heisenberg model and its analysis through finite-size scaling of Lee-Yang zeros. Besides the critical regime, we also investigate scaling in the ferromagnetic phase. We show that, in this case of broken symmetry, the corrections to scaling contain information on the Goldstone modes. We present a comprehensive Lee-Yang analysis, including the density of zeros and confirm recent numerical estimates for critical exponents.Comment: 19 pages, 9 figure

Griffiths singularities in the two dimensional diluted Ising model

We study numerically the probability distribution of the Yang-Lee zeroes inside the Griffiths phase for the two dimensional site diluted Ising model and we check that the shape of this distribution is that predicted in previous analytical works. By studying the finite size scaling of the averaged smallest zero at the phase transition we extract, for two values of the dilution, the anomalous dimension, $\eta$, which agrees very well with the previous estimated values.Comment: 11 pages and 4 figures, some minor changes in Fig. 4, available at http://chimera.roma1.infn.it/index_papers_complex.htm

Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump

It is numerically shown that the discontinuous character of the helicity modulus of the two-dimensional XY model at the Kosterlitz-Thouless (KT) transition can be directly related to a higher order derivative of the free energy without presuming any {\it a priori} knowledge of the nature of the transition. It is also suggested that this higher order derivative is of intrinsic interest in that it gives an additional characteristics of the KT transition which might be associated with a universal number akin to the universal value of the helicity modulus at the critical temperature.Comment: 4 pages, to appear in PR

Universality of the Ising Model on Sphere-like Lattices

We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes ranging up to O($10^5$) sites are simulated and finite size scaling is analyzed. The partition function zeros and the values of various cumulants at their respective peak positions are determined and they agree with the scaling behavior expected from universality with the Onsager solution on the torus ($\nu=1$). For the pseudocritical values of the coupling we find significant anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice topology.Comment: 24 pages, LaTeX, 8 figure

Fisher Renormalization for Logarithmic Corrections

For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.Comment: 10 pages, no figures. Version 2 has added reference

Is trivial the antiferromagnetic RP(2) model in four dimensions?

We study the antiferromagnetic RP(2) model in four dimensions. We find a second order transition with two order parameters, one ferromagnetic and the other antiferromagnetic. The antiferromagnetic sector has mean-field critical exponents and a renormalized coupling which goes to zero in the continuum limit. The exponents of the ferromagnetic channel are not the mean-field ones, but the difference can be interpreted as logarithmic corrections. We perform a detailed analysis of these corrections and conclude the triviality of the continuum limit of this model.Comment: 21 pages, 5 figures, LaTeX2

Altered retinal microRNA expression profile in a mouse model of retinitis pigmentosa

MicroRNA expression profiling showed that the retina of mice carrying a rhodopsin mutation that leads to retinitis pigmentosa have notably different microRNA profiles from wildtype mice; further in silico analyses identified potential retinal targets for differentially regulated microRNAs

Fisher's scaling relation above the upper critical dimension

Fisher's fluctuation-response relation is one of four famous scaling formulae and is consistent with a vanishing correlation-function anomalous dimension above the upper critical dimension d_c. However, it has long been known that numerical simulations deliver a negative value for the anomalous dimension there. Here, the apparent discrepancy is attributed to a distinction between the system-length and correlation- or characteristic-length scales. On the latter scale, the anomalous dimension indeed vanishes above d_c and Fisher's relation holds in its standard form. However, on the scale of the system length, the anomalous dimension is negative and Fisher's relation requires modification. Similar investigations at the upper critical dimension, where dangerous irrelevant variables become marginal, lead to an analogous pair of Fisher relations for logarithmic-correction exponents. Implications of a similar distinction between length scales in percolation theory above d_c and for the Ginzburg criterion are briefly discussed.Comment: Published version has 6 pages, 2 figure