Four-loop contributions to long-distance quantities in the two-dimensional nonlinear sigma-model on a square lattice: revised numerical estimates

We give the correct analytic expression of a finite integral appearing in the four-loop computation of the renormalization-group functions for the two-dimensional nonlinear sigma-model on the square lattice with standard action, explaining the origin of a numerical discrepancy. We revise the numerical expressions of Caracciolo and Pelissetto for the perturbative corrections of the susceptibility and of the correlation length. For the values used in Monte Carlo simulations, N=3, 4, 8, the second perturbative correction coefficient of the correlation length varies by 3%, 4%, 3% respectively. Other quantities vary similarly.Comment: 2 pages, Revtex, no figure

Application of a coordinate space method for the evaluation of lattice Feynman diagrams in two dimensions

We apply a new coordinate space method for the evaluation of lattice Feynman diagrams suggested by L\"uscher and Weisz to field theories in two dimensions. Our work is to be presented for the theories with massless propagators. The main idea is to deal with the integrals in position space by making use of the recursion relation for the free propagator $G(x)$ which allows to compute the propagator recursively by its values around origin. It turns out that the method is very efficient and gives very precise results. We illustrate the technique by evaluating a number of two- and three-loop diagrams explicitly.Comment: 25 pages, Latex, 2 figures, revised by discussing some points in more detail and correcting a few typo

Flocking together : collective animal minds in contemporary fiction

The remarkable coordination displayed by animal groups such as an ant colony or a flock of birds in flight is not just a behavioral feat; it reflects a full-fledged form of collective cognition. Building on work in philosophy, cognitive approaches to literature, and animal studies, I explore how contemporary fiction captures animal collectivity. I focus on three novels that probe different aspects of animal assemblages: animals as a collective agent (in Richard Powers's The Echo Maker), animals that communicate a shared mind through dance-like movements (in Lydia Davis's The Cows), and animals that embrace a collective "we" to critique the individualism of contemporary society (in Peter Verhelst's The Man I Became). When individuality drops out of the picture of human-animal encounters in fiction, empathy becomes abstract: a matter of quasi-geometric patterns that are experienced by readers through an embodied mechanism of kinesthetic resonance

Comparison between Theoretical Four-Loop Predictions and Monte Carlo Calculations in the Two-Dimensional NN-Vector Model for N=3,4,8N=3,4,8

We have computed the four-loop contribution to the beta-function and to the anomalous dimension of the field for the two-dimensional lattice $N$-vector model. This allows the determination of the second perturbative correction to various long-distance quantities like the correlation lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for $N = 3,4,8$. From these data we also extract the values of various universal nonperturbative constants, which we compare with the predictions of the $1/N$ expansion.Comment: 68456 bytes uuencoded gzip'ed (expands to 155611 bytes Postscript); 4 pages including all figures; contribution to Lattice '9

Composite operators from the operator product expansion: what can go wrong?

The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of systematic errors. The key problem turns out to be the violation of asymptotic scaling.Comment: Lattice 99 (Improvement and Renormalization), 3 pages, 3 eps figure

Testing the efficiency of different improvement programs

We study the finite-size behaviour of a tree-level on-shell improved action for the N-vector model. We present numerical results for N=3 and analytic results in the large-N limit for the mass gap. We also report a perturbative computation at one loop of the mass gap for states of spatial momentum p. We present a detailed comparison of the behaviour of this action with that of other formulations, including the perfect action, and a critical discussion of the different approaches to the problem of action improvement.Comment: LaTex2e, 34 pages, 5 ps figures, uses epsf, epsfig, amsfont, cite.st

Absence of sign problem in the (saddle point approximation of the) nilpotency expansion of QCD at finite chemical potential

We have developed a method to derive the (approximate) quark contribution to the fermion free energy of QCD on a lattice, at finite temperature and chemical potential, with Kogut-Susskind fermions in the flavor basis. We show here the expression at zero temperature. This result has been obtained at the lowest order of the nilpotency expansion. At this order the well known "sign problem" does not arise and the quark contribution to the action can be used as a statistical weight in the Monte Carlo simulations.Comment: 7 pages, presented at the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), Villasimius, Sardinia, Italy, June 14-19, 201

Asymptotically free models and discrete non-Abelian groups

We study the two-dimensional renormalization-group flow induced by perturbations that reduce the global symmetry of the O(3) sigma-model to the discrete symmetries of Platonic solids. We estimate the value of the correlation length at which differences in the behaviour of the various models should be expected. For the icosahedron model, we find xi > 200. We provide an explanation for the recent numerical results of Patrascioiu and Seiler and of Hasenfratz and Niedermayer.Comment: 12 pages, revised versio