The Weakly Coupled Gross-Neveu Model with Wilson Fermions

The nature of the phase transition in the lattice Gross-Neveu model with Wilson fermions is investigated using a new analytical technique. This involves a new type of weak coupling expansion which focuses on the partition function zeroes of the model. Its application to the single flavour Gross-Neveu model yields a phase diagram whose structure is consistent with that predicted from a saddle point approach. The existence of an Aoki phase is confirmed and its width in the weakly coupled region is determined. Parity, rather than chiral symmetry breaking naturally emerges as the driving mechanism for the phase transition.Comment: 15 pages including 1 figur

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

Soil Characterization at the Linde FUSRAP Site and the Impact on Soil Volume Estimates

The former Linde site in Tonawanda, New York is currently undergoing active remediation of Manhattan Engineering District's radiological contamination. This remediation is authorized under the Formerly Utilized Sites Remedial Action Program (FUSRAP). The focus of this paper will be to describe the impact of soil characterization efforts as they relate to soil volume estimates and project cost estimates. An additional objective is to stimulate discussion about other characterization and modeling technologies, and to provide a ''Lessons Learned'' scenario to assist in future volume estimating at other FUSRAP sites. Initial soil characterization efforts at the Linde FUSRAP site in areas known to be contaminated or suspected to be contaminated were presented in the Remedial Investigation Report for the Tonawanda Site, dated February 1993. Results of those initial characterization efforts were the basis for soil volume estimates that were used to estimate and negotiate the current remediation contract. During the course of remediation, previously unidentified areas of contamination were discovered, and additional characterization was initiated. Additional test pit and geoprobe samples were obtained at over 500 locations, bringing the total to over 800 sample locations at the 135-acre site. New data continues to be collected on a routine basis during ongoing remedial actions

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

The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk

The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for nonequilibrium dynamics, in particular driven diffusive processes. It is usually considered in a canonical ensemble in which the number of sites is fixed. We observe that the grand-canonical partition function for the ASEP is remarkably simple. It allows a simple direct derivation of the asymptotics of the canonical normalization in various phases and of the correspondence with One-Transit Walks recently observed by Brak et.al.Comment: Published versio

Ising spins coupled to a four-dimensional discrete Regge skeleton

Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model employed in this work limits the choice of the link lengths to a finite number. To get more precise insight into the behavior of the four-dimensional discrete Regge model, we coupled spins to the fluctuating manifolds. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field theory of the Ising model on a static four-dimensional lattice.Comment: 19 pages, 7 figure

Quasi-long-range ordering in a finite-size 2D Heisenberg model

We analyse the low-temperature behaviour of the Heisenberg model on a two-dimensional lattice of finite size. Presence of a residual magnetisation in a finite-size system enables us to use the spin wave approximation, which is known to give reliable results for the XY model at low temperatures T. For the system considered, we find that the spin-spin correlation function decays as 1/r^eta(T) for large separations r bringing about presence of a quasi-long-range ordering. We give analytic estimates for the exponent eta(T) in different regimes and support our findings by Monte Carlo simulations of the model on lattices of different sizes at different temperatures.Comment: 9 pages, 3 postscript figs, style files include

Fisher Zeroes and Singular Behaviour of the Two Dimensional Potts Model in the Thermodynamic Limit

The duality transformation is applied to the Fisher zeroes near the ferromagnetic critical point in the q>4 state two dimensional Potts model. A requirement that the locus of the duals of the zeroes be identical to the dual of the locus of zeroes in the thermodynamic limit (i) recovers the ratio of specific heat to internal energy discontinuity at criticality and the relationships between the discontinuities of higher cumulants and (ii) identifies duality with complex conjugation. Conjecturing that all zeroes governing ferromagnetic singular behaviour satisfy the latter requirement gives the full locus of such Fisher zeroes to be a circle. This locus, together with the density of zeroes is then shown to be sufficient to recover the singular form of the thermodynamic functions in the thermodynamic limit.Comment: 10 pages, 0 figures, LaTeX. Paper expanded and 2 references added clarifying duality relationships between discontinuities in higher cumulant

The protein arginine methyltransferase PRMT5 confers therapeutic resistance to mTOR inhibition in glioblastoma

IntroductionClinical trials directed at mechanistic target of rapamycin (mTOR) inhibition have yielded disappointing results in glioblastoma (GBM). A major mechanism of resistance involves the activation of a salvage pathway stimulating internal ribosome entry site (IRES)-mediated protein synthesis. PRMT5 activity has been implicated in the enhancement of IRES activity.MethodsWe analyzed the expression and activity of PRMT5 in response to mTOR inhibition in GBM cell lines and short-term patient cultures. To determine whether PRMT5 conferred resistance we used genetic and pharmacological approaches to ablate PRMT5 activity and assessed the effects on in vitro and in vivo sensitivity. Mutational analyses of the requisite IRES-trans-acting factor (ITAF), hnRNP A1 determined whether PRMT5-mediated methylation was necessary for ITAF RNA binding and IRES activity.ResultsPRMT5 activity is stimulated in response to mTOR inhibitors. Knockdown or treatment with a PRMT5 inhibitor blocked IRES activity and sensitizes GBM cells. Ectopic expression of non-methylatable hnRNP A1 mutants demonstrated that methylation of either arginine residues 218 or 225 was sufficient to maintain IRES binding and hnRNP A1-dependent cyclin D1 or c-MYC IRES activity, however a double R218K/R225K mutant was unable to do so. The PRMT5 inhibitor EPZ015666 displayed synergistic anti-GBM effects in vitro and in a xenograft mouse model in combination with PP242.ConclusionsThese results demonstrate that PRMT5 activity is stimulated upon mTOR inhibition in GBM. Our data further support a signaling cascade in which PRMT5-mediated methylation of hnRNP A1 promotes IRES RNA binding and activation of IRES-mediated protein synthesis and resultant mTOR inhibitor resistance

The Phases and Triviality of Scalar Quantum Electrodynamics

The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact. The phase diagram is two dimensional. No fine tuning or extrapolations are needed to study the theory's critical behovior. Two lines of second order phase transitions are discovered and the scaling laws for each are studied by finite size scaling methods on lattices ranging from $6^4$ through $24^4$. One line corresponds to monopole percolation and the other to a transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent specific heats. The lines of transitions cross in the interior of the phase diagram and appear to be unrelated. The monopole percolation transition has critical indices which are compatible with ordinary four dimensional percolation uneffected by interactions. Finite size scaling and histogram methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line are well-fit by the hypothesis that scalar quantum electrodynamics is logarithmically trivial. The logarithms are measured in both finite size scaling of the specific heat peaks as a function of volume as well as in the coupling constant dependence of the specific heats measured on fixed but large lattices. The theory is seen to be qualitatively similar to $\lambda\phi^{4}$. The standard CRAY random number generator RANF proved to be inadequateComment: 25pages,26figures;revtex;ILL-(TH)-94-#12; only hardcopy of figures availabl