Ground state non-universality in the random field Ising model

Two attractive and often used ideas, namely universality and the concept of a zero temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are non-universal. However, we also show that at finite temperature the thermal order parameter exponent one half is restored so that temperature is a relevant variable. The broader implications of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of two in Eq. 2., added a paragraph in conclusions for clarit

Properties of the random field Ising model in a transverse magnetic field

We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension $d > 2$, there is at low strength of randomness and transverse field, a phase with true long range order which is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e, the logarithm of the diverging time scale rises as a power of the diverging length scale

Neutralino-Nucleon Cross Section and Charge and Colour Breaking Constraints

We compute the neutralino-nucleon cross section in several supersymmetric scenarios, taking into account all kind of constraints. In particular, the constraints that the absence of dangerous charge and colour breaking minima imposes on the parameter space are studied in detail. In addition, the most recent experimental constraints, such as the lower bound on the Higgs mass, the $b\to s\gamma$ branching ratio, and the muon $g-2$ are considered. The astrophysical bounds on the dark matter density are also imposed on the theoretical computation of the relic neutralino density, assuming thermal production. This computation is relevant for the theoretical analysis of the direct detection of dark matter in current experiments. We consider first the supergravity scenario with universal soft terms and GUT scale. In this scenario the charge and colour breaking constraints turn out to be quite important, and \tan\beta\lsim 20 is forbidden. Larger values of $\tan\beta$ can also be forbidden, depending on the value of the trilinear parameter $A$. Finally, we study supergravity scenarios with an intermediate scale, and also with non-universal scalar and gaugino masses where the cross section can be very large.Comment: Final version to appear in JHE

The three-dimensional randomly dilute Ising model: Monte Carlo results

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices $L^3$ with $L\le 256$. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining $\nu = 0.683(3)$, $\eta = 0.035(2)$, $\beta = 0.3535(17)$, and $\alpha = -0.049(9)$, in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio $R^+_\xi$ that expresses the universality of the free-energy density per correlation volume. We find $R^+_\xi = 0.2885(15)$.Comment: 34 pages, 7 figs, few correction

Likelihood Functions for Supersymmetric Observables in Frequentist Analyses of the CMSSM and NUHM1

On the basis of frequentist analyses of experimental constraints from electroweak precision data, g-2, B physics and cosmological data, we investigate the parameters of the constrained MSSM (CMSSM) with universal soft supersymmetry-breaking mass parameters, and a model with common non-universal Higgs masses (NUHM1). We present chi^2 likelihood functions for the masses of supersymmetric particles and Higgs bosons, as well as b to s gamma, b to mu mu and the spin-independent dark matter scattering cross section. In the CMSSM we find preferences for sparticle masses that are relatively light. In the NUHM1 the best-fit values for many sparticle masses are even slightly smaller, but with greater uncertainties. The likelihood functions for most sparticle masses are cut off sharply at small masses, in particular by the LEP Higgs mass constraint. Both in the CMSSM and the NUHM1, the coannihilation region is favoured over the focus-point region at about the 3-sigma level, largely but not exclusively because of g-2. Many sparticle masses are highly correlated in both the CMSSM and NUHM1, and most of the regions preferred at the 95% C.L. are accessible to early LHC running. Some slepton and chargino/neutralino masses should be in reach at the ILC. The masses of the heavier Higgs bosons should be accessible at the LHC and the ILC in portions of the preferred regions in the (M_A, tan beta) plane. In the CMSSM, the likelihood function for b to mu mu is peaked close to the Standard Model value, but much larger values are possible in the NUHM1. We find that values of the DM cross section > 10^{-10} pb are preferred in both the CMSSM and the NUHM1. We study the effects of dropping the g-2, b to s gamma, relic density and M_h constraints.Comment: 34 pages, 24 figure

The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim L^\zeta$, is consistent with the theoretical prediction $\zeta = 2/3$. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales as for a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions. These dimensions are argued to be related to combinations of the energy scaling exponent, $\theta$, which determines the violation of hyperscaling, the correlation length exponent $\nu$, and the magnetization exponent $\beta$. The value $\beta = 0.017\pm 0.005$ is derived from the magnetization: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure

Squark-, Slepton- and Neutralino-Chargino coannihilation effects in the low-energy effective MSSM

Within the low-energy effective Minimal Supersymmetric extension of the Standard Model (effMSSM) we calculate the neutralino relic density taking into account slepton-neutralino, squark-neutralino and neutralino/chargino- neutralino coannihilation channels. By including squark (stop and sbottom) coannihilation channels we extend our comparative study to all allowed coannihilations and obtain the general result that all of them give sizable contributions to the reduction of the neutralino relic density. Due to these coannihilation processes some models (mostly with large neutralino masses) enter into the cosmologically interesting region for relic density, but other models leave this region. Nevertheless, in general, the predictions for direct and indirect dark matter detection rates are not strongly affected by these coannihilation channels in the effMSSM.Comment: 14 pages, 10 figures, corrected and to be published in Phys. Rev.

Dynamic structure factor of the Ising model with purely relaxational dynamics

We compute the dynamic structure factor for the Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the $\epsilon$ expansion, at two loops in the high-temperature phase and at one loop in the temperature magnetic-field plane, and a Monte Carlo simulation in the high-temperature phase. We find that the dynamic structure factor is very well approximated by its mean-field Gaussian form up to moderately large values of the frequency $\omega$ and momentum $k$. In the region we can investigate, $k\xi \lesssim 5$, $\omega \tau \lesssim 10$, where $\xi$ is the correlation length and $\tau$ the zero-momentum autocorrelation time, deviations are at most of a few percent.Comment: 21 pages, 3 figure

Slepton and Neutralino/Chargino Coannihilations in MSSM

Within the low-energy effective Minimal Supersymmetric extension of Standard Model (effMSSM) we calculated the neutralino relic density taking into account slepton-neutralino and neutralino-chargino/neutralino coannihilation channels. We performed comparative study of these channels and obtained that both of them give sizable contributions to the reduction of the relic density. Due to these coannihilation processes some models (mostly with large neutralino masses) enter into the cosmologically interesting region for relic density, but other models leave this region. Nevertheless, in general, the predictions for direct and indirect dark matter detection rates are not strongly affected by these coannihilation channels in the effMSSM.Comment: 12 pages, 9 figures, revte

Implications of LHC Searches on SUSY Particle Spectra: The pMSSM Parameter Space with Neutralino Dark Matter

We study the implications of LHC searches on SUSY particle spectra using flat scans of the 19-parameter pMSSM phase space. We apply constraints from flavour physics, g_mu-2, dark matter and earlier LEP and Tevatron searches. The sensitivity of the LHC SUSY searches with jets, leptons and missing energy is assessed by reproducing with fast simulation the recent CMS analyses after validation on benchmark points. We present results in terms of the fraction of pMSSM points compatible with all the constraints which are excluded by the LHC searches with 1 fb^{-1} and 15 fb^{-1} as a function of the mass of strongly and weakly interacting SUSY particles. We also discuss the suppression of Higgs production cross sections for the MSSM points not excluded and contrast the region of parameter space tested by the LHC data with the constraints from dark matter direct detection experiments.Comment: 14 pages, 13 figures. v2: increased statistics, to appear in EPJ