Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors

We study the nature of the multicritical point in the three-dimensional O(3)+O(2) symmetric Landau-Ginzburg-Wilson theory, which describes the competition of two order parameters that are O(3) and O(2) symmetric, respectively. This study is relevant for the SO(5) theory of high-Tc superconductors, which predicts the existence of a multicritical point in the temperature-doping phase diagram, where the antiferromagnetic and superconducting transition lines meet. We investigate whether the O(3)+O(2) symmetry gets effectively enlarged to O(5) approaching the multicritical point. For this purpose, we study the stability of the O(5) fixed point. By means of a Monte Carlo simulation, we show that the O(5) fixed point is unstable with respect to the spin-4 quartic perturbation with the crossover exponent $\phi_{4,4}=0.180(15)$, in substantial agreement with recent field-theoretical results. This estimate is much larger than the one-loop $\epsilon$-expansion estimate $\phi_{4,4}=1/26$, which has often been used in the literature to discuss the multicritical behavior within the SO(5) theory. Therefore, no symmetry enlargement is generically expected at the multicritical transition. We also perform a five-loop field-theoretical analysis of the renormalization-group flow. It shows that bicritical systems are not in the attraction domain of the stable decoupled fixed point. Thus, in these systems--high-Tc cuprates should belong to this class--the multicritical point corresponds to a first-order transition.Comment: 18 page

A Model for Force Fluctuations in Bead Packs

We study theoretically the complex network of forces that is responsible for the static structure and properties of granular materials. We present detailed calculations for a model in which the fluctuations in the force distribution arise because of variations in the contact angles and the constraints imposed by the force balance on each bead of the pile. We compare our results for force distribution function for this model, including exact results for certain contact angle probability distributions, with numerical simulations of force distributions in random sphere packings. This model reproduces many aspects of the force distribution observed both in experiment and in numerical simulations of sphere packings

Effective Potential for Scalar Field in Three Dimensions: Ising Model in the Ferromagnetic Phase

We compute the effective potential $V_{\rm eff}(\phi)$ for one-component real scalar field $\phi$ in three Euclidean dimensions (3D) in the case of spontaneously broken symmetry, from the Monte Carlo simulation of the 3D Ising model in external field at temperatures approaching the phase transition from below. We study probability distributions of the order parameter on the lattices from $30^3$ to $74^3$, at $L/\xi \approx 10$. We find that, in close analogy with the symmetric case, $\phi^6$ plays an important role: $V_{\rm eff}(\phi)$ is very well approximated by the sum of $\phi^2$, $\phi^4$ and $\phi^6$ terms. An unexpected feature is the negative sign of the $\phi^4$ term. As close to the continuum limit as we can get ($\xi \approx 7.2$), we obtain $${\cal L}_{\rm eff} \approx {1 \over 2} \partial_\mu \phi \partial_\mu \phi + 1.7 (\phi^2 - \eta^2)^2 (\phi^2 + \eta^2).$$ We also compute several universal coupling constants and ratios, including the combination of critical amplitudes $C^- (f_1^-)^{-3} B^{-2}$.Comment: 13 pages, 5 Postscript figures, uses epsf.st

New supersymmetric solutions of N=2, D=5 gauged supergravity with hyperscalars

We construct new supersymmetric solutions, including AdS bubbles, in an N=2 truncation of five-dimensional N=8 gauged supergravity. This particular truncation is given by N=2 gauged supergravity coupled to two vector multiples and three incomplete hypermultiplets, and was originally investigated in the context of obtaining regular AdS bubble geometries with multiple active R-charges. We focus on cohomogeneity-one solutions corresponding to objects with two equal angular momenta and up to three independent R-charges. Curiously, we find a new set of zero and negative mass solitons asymptotic to AdS_5/Z_k, for k \ge 3, which are everywhere regular without closed timelike curves.Comment: Latex 3 times, 42 page

Properties of Interfaces in the two and three dimensional Ising Model

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact $2D$ results. In the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical interfacial tension $F^s = F^s_0 t^\mu$ to be $F^s_0 = 1.52 \pm 0.05$. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.Comment: 25 pages; sorry no figures include

Field theory of bi- and tetracritical points: Statics

We calculate the static critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. Summation methods lead to fixed points describing multicritical behavior. Their stability boarder lines in the space of order parameter components $n_\|$ and $n_\perp$ and spatial dimension $d$ are calculated. The essential features obtained already in two loop order for the interesting case of an antiferromagnet in a magnetic field ($n_\|=1$, $n_\perp=2$) are the stability of the biconical fixed point and the neighborhood of the stability border lines to the other fixed points leading to very small transient exponents. We are also able to calculate the flow of static couplings, which allows to consider the attraction region. Depending on the nonuniversal background parameters the existence of different multicritical behavior (bicritical or tetracritical) is possible including a triple point.Comment: 6 figure

Plane waves with weak singularities

We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of divergence is such that the distortion suffered by a freely falling observer remains finite. Among such weak singular plane waves there is a sub-class which do not exhibit large back reaction in the presence of test scalar probes. String propagation in these backgrounds is smooth and there is a natural way to continue the metric beyond the singularity. This continued metric admits string propagation without the string becoming infinitely excited. We construct a one parameter family of smooth metrics which are at a finite distance in the space of metrics from the extended metric and a well defined operator in the string sigma model which resolves the singularity.Comment: 22 pages, Added references and clarifying comment

Critical specific heats of the N-vector spin models on the sc and the bcc lattices

We have computed through order $\beta^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,\beta)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic lattices. For this model, also known in quantum field theory as the lattice O(N) nonlinear sigma model, we have presented in previous papers extended expansions of the susceptibility, of its second field derivative and of the second moment of the correlation function. Here we study the internal specific energy and the specific heat $C(N,\beta)$, obtaining new estimates of the critical parameters and therefore a more accurate direct test of the hyperscaling relation $d \nu(N)=2 - \alpha(N)$ on a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. By the newly extended series, we also compute the universal combination of critical amplitudes usually denoted by $R^+_{\xi}(N)$, in fair agreement with renormalization group estimates.Comment: 15 pages, latex, no figure

Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices

For the classical N-vector model, with arbitrary N, we have computed through order \beta^{17} the high temperature expansions of the second field derivative of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body centered cubic lattices. (The N-vector model is also known as the O(N) symmetric classical spin Heisenberg model or, in quantum field theory, as the lattice O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on the two lattices, and by carefully allowing for the corrections to scaling, we obtain updated estimates of the critical parameters and more accurate tests of the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of values of the spin dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently extended series for the susceptibility and for the second correlation moment, we also compute the dimensionless renormalized four point coupling constants and some universal ratios of scaling correction amplitudes in fair agreement with recent renormalization group estimates.Comment: 23 pages, latex, no figure

Critical adsorption on curved objects

A systematic fieldtheoretic description of critical adsorption on curved objects such as spherical or rodlike colloidal particles immersed in a fluid near criticality is presented. The temperature dependence of the corresponding order parameter profiles and of the excess adsorption are calculated explicitly. Critical adsorption on elongated rods is substantially more pronounced than on spherical particles. It turns out that, within the context of critical phenomena in confined geometries, critical adsorption on a microscopically thin `needle' represents a distinct universality class of its own. Under favorable conditions the results are relevant for the flocculation of colloidal particles.Comment: 52 pages, 10 figure