Specific heat and energy for the three-dimensional O(2) model

We investigate the three-dimensional O(2) model on lattices of size 8^3 to 160^3 close to the critical point at zero magnetic field. We confirm explicitly the value of the critical coupling J_c found by Ballesteros et al. and estimate there the universal values of g_r and xi/L. At the critical point we study the finite size dependencies of the energy density epsilon and the specific heat C. We find that the nonsingular part of the specific heat C_{ns} is linearly dependent on 1/alpha. From the critical behaviour of the specific heat for T not T_c on the largest lattices we determine the universal amplitude ratio A+/A-. The alpha- dependence of this ratio is close to the phenomenological relation A+/A- = 1-4alpha.Comment: Lattice2001(spin), 3 pages, 4 figure

The chiral transition of N_f=2 QCD with fundamental and adjoint fermions

We study QCD with two staggered Dirac fermions both in the fundamental (QCD) and the adjoint representation (aQCD) near the chiral transition. The aim is to find the universality class of the chiral transition and to verify Goldstone effects below the transition. We investigate aQCD, because in that theory the deconfinement and the chiral transitions occur at different temperatures T_d<T_c. Here, we show that the scaling behaviour of the chiral condensate in the vicinity of \beta_c is in full agreeement with that of the 3d O(2) universality class. In the region T_d<T<T_c we confirm the quark mass dependence of the chiral condensate which is expected due to the existence of Goldstone modes like in 3d O(N) spin models. For fundamental QCD we use the p4-action. Here, we find Goldstone effects below T_c like in aQCD and the 3d O(N) spin models, however no O(2)/O(4) scaling near the chiral transition point. The result for QCD may be a consequence of the coincidence of the deconfinement transition with the chiral transition.Comment: 6 pages, 5 figures, poster contribution to Lattice 2005 (Nonzero temperature and density), one reference added, figure 2 change

Critical behaviour and Scaling functions for the three-dimensional O(6) spin model with external field

We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3 lattices. From Binder's cumulant at vanishing magnetic field we obtain the critical coupling J_c=1.42865(5) and verify this value with the \chi^2-method. The universal value of Binder's cumulant at this point is g_r(J_c)=-1.94456(10). At the critical coupling we find the critical exponents \nu=0.818(5), \beta=0.425(2) and \gamma=1.604(6) from a finite size scaling analysis. We also determine the finite-size-scaling function on the critical line and the equation of state. Our O(6)-result for the equation of state is compared to the Ising, O(2) and O(4) results.Comment: 5 pages, 4 figures, To appear in the proceedings of Workshop on Strong and Electroweak Matter (SEWM 2002), Heidelberg, Germany, 2-5 Oct 200

Comparison of finite-size-scaling functions for 3d O(N) spin models to QCD

We calculate numerically universal finite-size-scaling functions of the magnetization for the three-dimensional O(4) and O(2) spin models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.Comment: Lattice2001(hightemp), 3 pages, 5 figures, acknowledgements completed, minor typographical errors correcte

A numerical study of Goldstone-mode effects and scaling functions of the three-dimensional O(2) model

We investigate numerically the three-dimensional O(2) model on 8^3-160^3 lattices as a function of the magnetic field H. In the low-temperature phase we verify the H-dependence of the magnetization M induced by the Goldstone modes and determine M in the thermodynamic limit on the coexistence line both by extrapolation and by chiral perturbation theory. We compute two critical amplitudes from the scaling behaviours on the coexistence line and on the critical line. In both cases we find negative corrections to scaling. With additional high temperature data we calculate the scaling function and show that it has a smaller slope than that of the O(4) model. For future tests of QCD lattice data we study as well finite-size-scaling functions.Comment: Lattice 2000 (Spin Models), minor typographic errors fixe

Scaling and Goldstone effects in a QCD with two flavours of adjoint quarks

We study QCD with two Dirac fermions in the adjoint representation at finite temperature by Monte Carlo simulations.In such a theory the deconfinement and chiral phase transitions occur at different temperatures. We locate the second order chiral transition point at beta_c=5.624(2) and show that the scaling behaviour of the chiral condensate in the vicinity of beta_c is in full agreeement with that of the 3d O(2) universality class, and to a smaller extent comparable to the 3d O(6) class. From the previously determined first order deconfinement transition point beta_d=5.236(3) and the two-loop beta function we find the ratio T_c/T_d = 7.8(2). In the region between the two phase transitions we explicitly confirm the quark mass dependence of the chiral condensate which is expected due to the existence of Goldstone modes like in 3d O(N) spin models. At the deconfinement transition the condensate shows a gap, and below beta_d, it is nearly mass-independent for fixed beta.Comment: 28 pages, 12 figures, Latex2

Reggeon and pion contributions in semi-exclusive diffractive processes at HERA

A detailed analysis of semi-exclusive diffractive processes in e-p DIS at HERA, with the diffractive final states in the forward direction is presented. The contributions of the subleading f_2, \omega, a_2, \rho reggeons and the pion exchanges to the diffractive structure function with the forward proton or neutron are estimated. It is found that the (a_2,\rho) reggeons are entirely responsible for the forward neutron production at x_P < 10^{-3}. The \pi N production in the forward region is estimated using the Deck mechanism. The significance of this reaction for the processes measured at HERA, especially with the leading neutron, is discussed.Comment: Strongly revised version accepted for publication in Phys.Rev.D. Latex, 14 pages with 5 eps figures include

Finite-size-scaling functions for 3d O(4) and O(2) spin models and QCD

We calculate numerically universal finite-size-scaling functions for the three-dimensional O(4) and O(2) models. The approach of these functions to the infinite-volume scaling functions is studied in detail on the critical and pseudocritical lines. For this purpose we determine the pseudocritical line in two different ways. We find that the asymptotic form of the finite-size-scaling functions is already reached at small values of the scaling variable. A comparison with QCD lattice data for two flavours of staggered fermions shows a similar finite-size behaviour which is compatible with that of the spin models.Comment: 14 pages, 14 Ps-figures, Latex2