12,114 research outputs found

    A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class

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    We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up to L=360 to obtain accurate estimates for critical exponents. We focus on values of D, where the amplitudes of leading corrections are small. Furthermore we employ improved observables that have a small amplitude of the leading correction. We obtain nu=0.63002(10), eta=0.03627(10) and omega=0.832(6). We compare our results with those obtained from previous Monte Carlo simulations and high temperature series expansions of lattice models, by using field theoretic methods and experiments.Comment: 25 pages, 6 figures, typos corrected, references added, conclusions extende

    Mott Transition in Quasi-One-Dimensional Systems

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    We report the application of the density-matrix renormalization group method to a spatially anisotropic two-dimensional Hubbard model at half-filling. We find a deconfinement transition induced by the transverse hopping parameter tyt_y from an insulator to a metal. Therefore, if tyt_y is fixed in the metallic phase, increasing the interaction UU leads to a metal-to-insulator transition at a finite critical UU. This is in contrast to the weak-coupling Hartree-Fock theory which predicts a nesting induced antiferromagnetic insulator for any U>0U>0.Comment: 4 pages, 3 figure

    On the universality class of the Mott transition in two dimensions

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    We use the two-step density-matrix renormalization group method to elucidate the long-standing issue of the universality class of the Mott transition in the Hubbard model in two dimensions. We studied a spatially anisotropic two-dimensional Hubbard model with a non-perfectly nested Fermi surface at half-filling. We find that unlike the pure one-dimensional case where there is no metallic phase, the quasi one-dimensional modeldisplays a genuine metal-insulator transition at a finite value of the interaction. The critical exponent of the correlation length is found to be ν1.0\nu \approx 1.0. This implies that the fermionic Mott transition, belongs to the universality class of the 2D Ising model. The Mott insulator is the 'ordered' phase whose order parameter is given by the density of singly occupied sites minus that of holes and doubly occupied sites.Comment: 9 pages, 8 figure

    Universal amplitude ratios in the 3D Ising Universality Class

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    We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain A_+/A_-=0.536(2) and C_+/C_-=4.713(7), where A_+- and C_+- are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts + and - indicate the high and the low temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high and low temperature series expansions, field theoretic methods and experiments.Comment: 18 pages, two figures, typos corrected, discussion on finite size corrections extende

    Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model

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    Motivated by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of ρs12L\rho_{s1} 2L and ρs22L\rho_{s2} 2L, where LL stands for the spatial box size used in the simulations and ρsi\rho_{si} with i{1,2}i \in \{1,2\} is the spin-stiffness in the ii-direction. Remarkably, while we do observe a large correction to scaling for the observable ρs12L\rho_{s1}2L as proposed in \cite{Fritz11}, the data for ρs22L\rho_{s2}2L exhibit a good scaling behavior without any indication of a large correction. As a consequence, we are able to obtain a numerical value for the critical exponent ν\nu which is consistent with the known O(3) result with moderate computational effort. Specifically, the numerical value of ν\nu we determine by fitting the data points of ρs22L\rho_{s2}2L to their expected scaling form is given by ν=0.7120(16)\nu=0.7120(16), which agrees quantitatively with the most accurate known Monte Carlo O(3) result ν=0.7112(5)\nu = 0.7112(5). Finally, while we can also obtain a result of ν\nu from the observable second Binder ratio Q2Q_2 which is consistent with ν=0.7112(5)\nu=0.7112(5), the uncertainty of ν\nu calculated from Q2Q_2 is more than twice as large as that of ν\nu determined from ρs22L\rho_{s2}2L.Comment: 7 figures, 1 table; brief repor

    Evidence for O(2) universality at the finite temperature transition for lattice QCD with 2 flavours of massless staggered quarks

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    We simulate lattice QCD with 2 flavours of massless quarks on lattices of temporal extent N_t=8, to study the finite temperature transition from hadronic matter to a quark-gluon plasma. A modified action which incorporates an irrelevant chiral 4-fermion interaction is used, which allows simulations at zero quark mass. We obtain excellent fits of the chiral condensates to the magnetizations of a 3-dimensional O(2) spin model on lattices small enough to model the finite size effects. This gives predictions for correlation lengths and chiral susceptibilities from the corresponding spin-model quantities. These are in good agreement with our measurements over the relevant range of parameters. Binder cumulants are measured, but the errors are too large to draw definite conclusions. From the properties of the O(2) spin model on the relatively small lattices with which we fit our `data', we can see why earlier attempts to fit staggered lattice data to leading-order infinite-volume scaling functions, as well as finite size scaling studies, failed and led to erroneous conclusions.Comment: 27 pages, Latex with 10 postscript figures. Some of the discussions have been expanded to satisfy a referee. Typographical errors were correcte

    Interplay between temperature and trap effects in one-dimensional lattice systems of bosonic particles

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    We investigate the interplay of temperature and trap effects in cold particle systems at their quantum critical regime, such as cold bosonic atoms in optical lattices at the transitions between Mott-insulator and superfluid phases. The theoretical framework is provided by the one-dimensional Bose-Hubbard model in the presence of an external trapping potential, and the trap-size scaling theory describing the large trap-size behavior at a quantum critical point. We present numerical results for the low-temperature behavior of the particle density and the density-density correlation function at the Mott transitions, and within the gapless superfluid phase.Comment: 9 page

    Slow dynamics at the smeared phase transition of randomly layered magnets

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    We investigate a model for randomly layered magnets, viz. a three-dimensional Ising model with planar defects. The magnetic phase transition in this system is smeared because static long-range order can develop on isolated rare spatial regions. Here, we report large-scale kinetic Monte Carlo simulations of the dynamical behavior close to the smeared phase transition which we characterize by the spin (time) autocorrelation function. In the paramagnetic phase, its behavior is dominated by Griffiths effects similar to those in magnets with point defects. In the tail region of the smeared transition the dynamics is even slower: the autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small asymptotic value following a power law at late times. Our Monte-Carlo results are in good agreement with recent theoretical predictions based on optimal fluctuation theory.Comment: 7 pages, 6 eps figures, final version as publishe

    Phase structure of lattice QCD with two flavors of Wilson quarks at finite temperature and chemical potential

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    We present results for phase structure of lattice QCD with two degenerate flavors (Nf=2N_f=2) of Wilson quarks at finite temperature TT and small baryon chemical potential μB\mu_B. Using the imaginary chemical potential for which the fermion determinant is positive, we perform simulations at points where the ratios of pseudo-scalar meson mass to the vector meson mass mπ/mρm_\pi/m_\rho are between 0.943(3)0.943(3) and 0.899(4)0.899(4) as well as in the quenched limit. By analytic continuation to real quark chemical potential μ\mu, we obtain the transition temperature as a function of small μB\mu_B. We attempt to determine the nature of transition at imaginary chemical potential by histogram, MC history, and finite size scaling. In the infinite heavy quark limit, the transition is of first order. At intermediate values of quark mass mqm_q corresponding to the ratio of mπ/mρm_\pi/m_\rho in the range from 0.943(3)0.943(3) to 0.899(4)0.899(4) at aμI=0.24a\mu_I=0.24, the MC simulations show absence of phase transition.Comment: 10 pages, 17 figures;16 figures;9 pages,10 figures;10 pages,11 figure

    Composition-tuned smeared phase transitions

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    Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. In this paper, we study such smeared phase transitions (both classical and quantum) in substitutional alloys A1x_{1-x}Bx_x that can be tuned from an ordered phase at composition x=0x=0 to a disordered phase at x=1x=1. We show that the ordered phase develops a pronounced tail that extends over all compositions x<1x<1. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also compare our results to computer simulations of a toy model, and we discuss experiments.Comment: 6 pages, 4 eps figures included, final version as publishe
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