Critical behavior of the three-dimensional bond-diluted Ising spin glass: Finite-size scaling functions and Universality

We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution p*, at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.Comment: Revised version. 10 pages, 9 figures, 2 table

Casimir force in the rotor model with twisted boundary conditions

We investigate the three dimensional lattice XY model with nearest neighbor interaction. The vector order parameter of this system lies on the vertices of a cubic lattice, which is embedded in a system with a film geometry. The orientations of the vectors are fixed at the two opposite sides of the film. The angle between the vectors at the two boundaries is $\alpha$ where $0 \le \alpha \le \pi$. We make use of the mean field approximation to study the mean length and orientation of the vector order parameter throughout the film---and the Casimir force it generates---as a function of the temperature $T$, the angle $\alpha$, and the thickness $L$ of the system. Among the results of that calculation are a Casimir force that depends in a continuous way on both the parameter $\alpha$ and the temperature and that can be attractive or repulsive. In particular, by varying $\alpha$ and/or $T$ one controls \underline{both} the sign \underline{and} the magnitude of the Casimir force in a reversible way. Furthermore, for the case $\alpha=\pi$, we discover an additional phase transition occurring only in the finite system associated with the variation of the orientations of the vectors.Comment: 14 pages, 9 figure

The critical behavior of 3D Ising glass models: universality and scaling corrections

We perform high-statistics Monte Carlo simulations of three three-dimensional Ising spin-glass models: the +-J Ising model for two values of the disorder parameter p, p=1/2 and p=0.7, and the bond-diluted +-J model for bond-occupation probability p_b = 0.45. A finite-size scaling analysis of the quartic cumulants at the critical point shows conclusively that these models belong to the same universality class and allows us to estimate the scaling-correction exponent omega related to the leading irrelevant operator, omega=1.0(1). We also determine the critical exponents nu and eta. Taking into account the scaling corrections, we obtain nu=2.53(8) and eta=-0.384(9).Comment: 9 pages, published versio

Universality class of 3D site-diluted and bond-diluted Ising systems

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, $\nu=0.683(2)$, $\eta=0.036(1)$, $\alpha=-0.049(6)$, $\gamma=1.341(4)$, $\beta=0.354(1)$, $\delta=4.792(6)$, and of the leading and next-to-leading correction-to-scaling exponents, $\omega=0.33(3)$ and $\omega_2=0.82(8)$.Comment: 45 pages, 22 figs, revised estimate of n

Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate

Motivated by recent experiments with confined binary liquid mixtures near demixing, we study the universal critical properties of a system, which belongs to the Ising universality class, in the film geometry. We employ periodic boundary conditions in the two lateral directions and fixed boundary conditions on the two confining surfaces, such that one of them has a spatially homogeneous adsorption preference while the other one exhibits a laterally alternating adsorption preference, resembling locally a single chemical step. By means of Monte Carlo simulations of an improved Hamiltonian, so that the leading scaling corrections are suppressed, numerical integration, and finite-size scaling analysis we determine the critical Casimir force and its universal scaling function for various values of the aspect ratio of the film. In the limit of a vanishing aspect ratio the critical Casimir force of this system reduces to the mean value of the critical Casimir force for laterally homogeneous ++ and +- boundary conditions, corresponding to the surface spins on the two surfaces being fixed to equal and opposite values, respectively. We show that the universal scaling function of the critical Casimir force for small but finite aspect ratios displays a linear dependence on the aspect ratio which is solely due to the presence of the lateral inhomogeneity. We also analyze the order-parameter profiles at criticality and their universal scaling function which allows us to probe theoretical predictions and to compare with experimental data.Comment: revised version, section 5.2 expanded; 53 pages, 12 figures, iopart clas

The 3-D O(4) universality class and the phase transition in two-flavor QCD

We determine the critical equation of state of the three-dimensional O(4) universality class. We first consider the small-field expansion of the effective potential (Helmholtz free energy). Then, we apply a systematic approximation scheme based on polynomial parametric representations that are valid in the whole critical regime, satisfy the correct analytic properties (Griffiths' analyticity), take into account the Goldstone singularities at the coexistence curve, and match the small-field expansion of the effective potential. From the approximate representations of the equation of state, we obtain estimates of several universal amplitude ratios. The three-dimensional O(4) universality class is expected to describe the finite-temperature chiral transition of quantum chromodynamics with two light flavors. Within this picture, the O(4) critical equation of state relates the reduced temperature, the quark masses, and the condensates around T_c in the limit of vanishing quark masses.Comment: 19 pages, 5 fig

Critical behavior of the random-anisotropy model in the strong-anisotropy limit

We investigate the nature of the critical behavior of the random-anisotropy Heisenberg model (RAM), which describes a magnetic system with random uniaxial single-site anisotropy, such as some amorphous alloys of rare earths and transition metals. In particular, we consider the strong-anisotropy limit (SRAM), in which the Hamiltonian can be rewritten as the one of an Ising spin-glass model with correlated bond disorder. We perform Monte Carlo simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring correlation functions of the replica-replica overlap, which is the order parameter at a glass transition. The corresponding results show critical behavior and finite-size scaling. They provide evidence of a finite-temperature continuous transition with critical exponents $\eta_o=-0.24(4)$ and $\nu_o=2.4(6)$. These results are close to the corresponding estimates that have been obtained in the usual Ising spin-glass model with uncorrelated bond disorder, suggesting that the two models belong to the same universality class. We also determine the leading correction-to-scaling exponent finding $\omega = 1.0(4)$.Comment: 24 pages, 13 figs, J. Stat. Mech. in pres

On the nature of the finite-temperature transition in QCD

We discuss the nature of the finite-temperature transition in QCD with N_f massless flavors. Universality arguments show that a continuous (second-order) transition must be related to a 3-D universality class characterized by a complex N_f X N_f matrix order parameter and by the symmetry-breaking pattern [SU(N_f)_L X SU(N_f)_R]/Z(N_f)_V -> SU(N_f)_V/Z(N_f)_V, or [U(N_f)_L X U(N_f)_R]/U(1)_V -> U(N_f)_V/U(1)_V if the U(1)_A symmetry is effectively restored at T_c. The existence of any of these universality classes requires the presence of a stable fixed point in the corresponding 3-D Phi^4 theory with the expected symmetry-breaking pattern. Otherwise, the transition is of first order. In order to search for stable fixed points in these Phi^4 theories, we exploit a 3-D perturbative approach in which physical quantities are expanded in powers of appropriate renormalized quartic couplings. We compute the corresponding Callan-Symanzik beta-functions to six loops. We also determine the large-order behavior to further constrain the analysis. No stable fixed point is found, except for N_f=2, corresponding to the symmetry-breaking pattern [SU(2)_L X SU(2)_R]/Z(2)_V -> SU(2)_V/Z(2)_V equivalent to O(4) -> O(3). Our results confirm and put on a firmer ground earlier analyses performed close to four dimensions, based on first-order calculations in the framework of the epsilon=4-d expansion. These results indicate that the finite-temperature phase transition in QCD is of first order for N_f>2. A continuous transition is allowed only for N_f=2. But, since the theory with symmetry-breaking pattern [U(2)_L X U(2)_R]/U(1)_V -> U(2)_V/U(1)_V does not have stable fixed points, the transition can be continuous only if the effective breaking of the U(1)_A symmetry is sufficiently large.Comment: 30 pages, 3 figs, minor correction

The Functional Renormalization Group and O(4) scaling

The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale dependent thermodynamic potential at finite temperature and density in the presence of a symmetry-breaking external field. Within this scheme, the critical scaling behavior of the order parameter, its transverse and longitudinal susceptibilities as well as the correlation lengths near the chiral phase transition are computed. We focus on the scaling properties of these observables at non-vanishing external field when approaching the critical point from the symmetric as well as from the broken phase. We confront our numerical results with the Widom-Griffiths form of the magnetic equation of state, obtained by a systematic epsilon-expansion of the scaling function. Our results for the critical exponents are consistent with those recently computed within Lattice Monte-Carlo studies of the O(4) spin system.Comment: 14 pages, 11 figure

Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model

We consider the random-bond +- J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T*= 0.9527(1), p*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T=0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T<T*, that the transitions are continuous and controlled by a strong-disorder fixed point with critical exponents nu=1.50(4) and eta=0.128(8), and beta = 0.095(5). This fixed point is definitely different from the Ising fixed point controlling the paramagnetic-ferromagnetic transitions for T>T*. Our results for the critical exponents are consistent with the hyperscaling relation 2 beta/nu - eta = d - 2 = 0.Comment: 32 pages, added refs and a discussion on hyperscalin