Showing papers by "Ettore Vicari published in 2001"
TL;DR: In this article, the authors improved the theoretical estimates of the critical exponents for the three-dimensional universality class by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions.
Abstract: We improve the theoretical estimates of the critical exponents for the three-dimensional $\mathrm{XY}$ universality class. We find $\ensuremath{\alpha}=\ensuremath{-}0.0146(8),$ $\ensuremath{\gamma}=1.3177(5),$ $\ensuremath{
u}=0.67155(27),$ $\ensuremath{\eta}=0.0380(4),$ $\ensuremath{\beta}=0.3485(2),$ and $\ensuremath{\delta}=4.780(2).$ We observe a discrepancy with the most recent experimental estimate of $\ensuremath{\alpha};$ this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.
300 citations
TL;DR: In this article, the critical behavior of frustrated spin models with noncollinear order was studied, including stacked triangular antiferromagnets and helimagnets, and the existence of a stable fixed point that corresponds to the conjectured chiral universality class was shown.
Abstract: We study the critical behavior of frustrated spin models with noncollinear order, including stacked triangular antiferromagnets and helimagnets. For this purpose we compute the field-theoretic expansions at a fixed dimension to six loops and determine their large-order behavior. For the physically relevant cases of two and three components, we show the existence of a stable fixed point that corresponds to the conjectured chiral universality class. This contradicts previous three-loop field-theoretical results but is in agreement with experiments.
78 citations
TL;DR: In this article, the spectrum of the confining strings of the SU(6) gauge theory was studied and the three independent string tensions related to sources with ${Z}_{N}$ charge $k=1,2,3,$ using Monte Carlo simulations.
Abstract: In the context of four-dimensional $\mathrm{SU}(N)$ gauge theories, we study the spectrum of the confining strings. We compute, for the SU(6) gauge theory formulated on a lattice, the three independent string tensions ${\ensuremath{\sigma}}_{k}$ related to sources with ${Z}_{N}$ charge $k=1,2,3,$ using Monte Carlo simulations. Our results, whose uncertainty is approximately 2% for $k=2$ and 4% for $k=3,$ are consistent with the sine formula ${\ensuremath{\sigma}}_{k}/\ensuremath{\sigma}=\mathrm{sin}(k\ensuremath{\pi}/N)/\mathrm{sin}(\ensuremath{\pi}/N)$ for the ratio between ${\ensuremath{\sigma}}_{k}$ and the standard string tension \ensuremath{\sigma}, and show deviations from the Casimir scaling. The sine formula is known to emerge in supersymmetric $\mathrm{SU}(N)$ gauge theories and in M theory. We comment on an analogous behavior exhibited by two-dimensional $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(N)$ chiral models.
70 citations
TL;DR: In this paper, the authors considered the Landau-Ginzburg-Wilson Hamiltonian with O(n)x O(m) symmetry and computed the critical exponents at all fixed points.
69 citations
TL;DR: In this paper, the authors consider the Landau-Ginzburg-Wilson Hamiltonian with O(n)x O(m) symmetry and compute the critical exponents at all fixed points to O (n^{-2}) and O(epsilon^3) in a \epsilone=4-d expansion.
Abstract: We consider the Landau-Ginzburg-Wilson Hamiltonian with O(n)x O(m) symmetry and compute the critical exponents at all fixed points to O(n^{-2}) and to O(\epsilon^3) in a \epsilon=4-d expansion. We also consider the corresponding non-linear sigma model and determine the fixed points and the critical exponents to O(\tilde{\epsilon}^2) in the \tilde{\epsilon}=d-2 expansion. Using these results, we draw quite general conclusions on the fixed-point structure of models with O(n)xO(m) symmetry for n large and all 2 < d < 4.
58 citations
TL;DR: In this paper, the chiral critical exponents for frustrated two-and three-component spin systems with noncollinear order, such as stacked triangular antiferromagnets (STA), were computed and analyzed.
Abstract: We compute the chiral critical exponents for the chiral transition in frustrated two- and three-component spin systems with noncollinear order, such as stacked triangular antiferromagnets (STA). For this purpose, we calculate and analyze the six-loop field-theoretical expansion of the renormalization-group function associated with the chiral operator. The results are in satisfactory agreement with those obtained in the recent experiment on the $\mathrm{XY}$ STA ${\mathrm{CsMnBr}}_{3}$ reported by [V. P. Plakhty et al., Phys. Rev. Lett. 85, 3942 (2000)], providing further support for the continuous nature of the chiral transition.
33 citations
TL;DR: In this paper, the 2n-point coupling constants in the high-temperature phase of the two-dimensional Ising model were computed by using transfer-matrix techniques, which provided the first few terms of the expansion of the effective potential (Helmholtz free energy) and of the equation of state in terms of renormalized magnetization.
Abstract: We compute the 2n-point coupling constants in the high-temperature phase of the two-dimensional Ising model by using transfer-matrix techniques. This provides the first few terms of the expansion of the effective potential (Helmholtz free energy) and of the equation of state in terms of the renormalized magnetization. By means of a suitable parametric representation, we determine an analytic extension of these expansions, providing the equation of state in the whole critical region in the t,h plane.
30 citations
12 citations
TL;DR: P phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal crossover behavior of the data for any finite range are determined.
Abstract: We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, which corresponds to the limit $\stackrel{\ensuremath{\rightarrow}}{N}0$ of an N-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed by using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions for the critical crossover functions, finding good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal crossover behavior of our data for any finite range.
11 citations
01 Jan 2001
TL;DR: In this paper, the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point was studied in a model of self-avoiding walks with medium-range jumps.
Abstract: We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, which corresponds to the limit N-->0 of an N-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed by using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions for the critical crossover functions, finding good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal crossover behavior of our data for any finite range.
9 citations
TL;DR: In this article, the authors classify the possible irrelevant operators for the Ising model on the square and triangular lattices and analyze the existing results for the free energy and its derivatives, showing that they are in agreement with the conformal-field theory predictions.
Abstract: By using conformal-field theory, we classify the possible irrelevant operators for the Ising model on the square and triangular lattices. We analyze the existing results for the free energy and its derivatives and for the correlation length, showing that they are in agreement with the conformal-field theory predictions. Moreover, these results imply that the nonlinear scaling field of the energy-momentum tensor vanishes at the critical point. Several other peculiar cancellations are explained in terms of a number of general conjectures. We show that all existing results on the square and triangular lattice are consistent with the assumption that only nonzero spin operators are present.
TL;DR: In this paper, the spectrum of the confining strings in four-dimensional SU(N) gauge theories was studied and the sine formula sigma_k/sigma = sin k pi/N/N / sin pi/n/N for the ratio between sigma-k and the standard string tension sigma.
Abstract: We study the spectrum of the confining strings in four-dimensional SU(N) gauge theories. We compute, for the SU(4) and SU(6) gauge theories formulated on a lattice, the string tensions sigma_k related to sources with Z_N charge k, using Monte Carlo simulations. Our results are consistent with the sine formula sigma_k/sigma = sin k pi/N / sin pi/N for the ratio between sigma_k and the standard string tension sigma.
For the SU(4) and SU(6) cases the accuracy is approximately 1% and 2%, respectively. The sine formula is known to emerge in various realizations of supersymmetric SU(N) gauge theories. On the other hand, our results show deviations from Casimir scaling. We also discuss an analogous behavior exhibited by two-dimensional SU(N) x SU(N) chiral models.
01 Mar 2001
TL;DR: In this paper, a combination of high-temperature expansions and Monte Carlo simulations is used to study three-dimensional spin models of the Ising and XY universality classes, and scaling amplitude ratios are computed via the critical equation of state.
Abstract: Three-dimensional spin models of the Ising and XY universality classes are studied by a combination of high-temperature expansions and Monte Carlo simulations. Critical exponents are determined to very high precision. Scaling amplitude ratios are computed via the critical equation of state. Our results are compared with other theoretical computations and with experiments, with special emphasis on the λ transition of 4 He.
TL;DR: In this paper, a combination of high-temperature expansions and Monte Carlo simulations applied to improved Hamiltonians is used to determine the critical exponents and the critical equation of state of the Ising and XY universality classes.
Abstract: Three-dimensional spin models of the Ising and XY universality classes are studied by a combination of high-temperature expansions and Monte Carlo simulations applied to improved Hamiltonians. The critical exponents and the critical equation of state are determined to very high precision.
01 Jan 2001
TL;DR: In this article, the authors consider the fixed-dimension perturbative expansion and discuss the nonanalyticity of the renormalization-group functions at the fixed point and its consequences for the numerical determination of critical quantities.
Abstract: We consider the fixed-dimension perturbative expansion. We discuss the nonanalyticity of the renormalization-group functions at the fixed point and its consequences for the numerical determination of critical quantities.
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TL;DR: In this paper, the four-dimensional SU(4 and SU(6) gauge theories were formulated on a lattice and the string tensions sigma_k related to sources with Z_N charge k were computed using Monte Carlo simulations.
Abstract: We compute, for the four-dimensional SU(4) and SU(6) gauge theories formulated on a lattice, the string tensions sigma_k related to sources with Z_N charge k, using Monte Carlo simulations. Our results are compatible with sigma_k \propto sin (k pi/N), and show sizeable deviations from Casimir scaling.
TL;DR: In this paper, the structure factor and the monomer-monomer distribution function for ring polymers in good solvents in the dilute limit were determined and the asymptotic behavior of these functions for small and large momenta and distances by using field-theoretical methods.
Abstract: We consider ring polymers in good solvents in the dilute limit. We determine the structure factor and the monomer-monomer distribution function. We compute accurately the asymptotic behavior of these functions for small and large momenta and distances by using field-theoretical methods. Phenomenological expressions with the correct asymptotic behaviors are also given.