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The reweighting method is widely used in numerical studies of QCD, in particular, for the cases in which the conventional Monte-Carlo method cannot be applied directly, e.g., finite density QCD. However, the application range of the reweighing method is restricted due to several problems. One of the most severe problems here is the overlap problem. To solve it, we examine a multipoint reweighting method in which simulations at several simulation points are combined in the data analyses. We systematically study the applicability and limitation of the multipoint reweighting method in two-flavor QCD at zero density. Measuring histograms of physical quantities at a series of simulation points, we apply the multipoint reweighting method to calculate the meson masses as continuous functions of the gauge coupling $\beta$ and the hopping parameters $\kappa$. We then determine lines of constant physics and beta functions, which are needed in a calculation of the equation of state at finite temperature., Comment: 16 pages, 25 figures. arXiv admin note: text overlap with arXiv:1501.06331

We present results for mesonic propagators in temporal and spatial direction and for topological properties at T below and above the deconfining transition in quenched QCD. We use anisotropic lattices and Wilson fermions., Comment: 6 pages, 7 figures, Talk given at 16th International Symposium on Lattice Field Theory (LATTICE 98(hightemp)) , Boulder, CO, 13-18 Jul 1998. (Replaced: Fig.4 corrected, further minor modifications in legends and text.)

We study thermodynamic properties of 2+1 flavor QCD with improved Wilson quarks coupled with the RG improved Iwasaki glue, using the fixed scale approach. We present the results for the equation of state, renormalized Polyakov loop, and chiral condensate., Comment: 7 pages, 7 figures, proceedings of the 30th International Symposium on Lattice Field Theory, June 24-29, 2012, Cairns, Australia

We extend our previous study of the QCD phase structure in the heavy quark region to non-zero chemical potentials. To identify the critical point where the first order deconfining transition terminates, we study an effective potential defined by the probability distribution function of the plaquette and the Polyakov loop. The reweighting technique is shown to be powerful in evaluating the effective potential in a wide range of the plaquette and Polyakov loop expectation values. We adopt the cumulant expansion to overcome the sign problem in the calculation of complex phase of the quark determinant. We find that the method provides us with an intuitive and powerful way to study the phase structure. We estimate the location of the critical point at finite chemical potential in the heavy quark region., Comment: 7 pages, 7 figures; XXIX International Symposium on Lattice Field Theory - Lattice 2011

It is shown that a series of solvable polynomials is attached to the series of zero modes constructed by Adam, Muratori and Nash \cite{AdamMuratoriNash1, Comment: 13 pages

We study the quark mass dependence of the finite temperature QCD phase transition in the heavy quark region using an effective potential defined through the probability distribution function of the average plaquette. Performing a simulation of SU(3) pure gauge theory, we first confirm that the distribution function has two peaks indicating that the phase transition is of first order in the heavy quark limit, while the first order transition turns into a crossover as the quark mass decreases from infinity, where the mass dependence of the distribution function is evaluated by the reweighting method combined with the hopping parameter expansion. We determine the endpoint of the first order transition region for N_f=1, 2, 3 and 2+1 cases. The quark mass dependence of the latent heat is also evaluated in the first order transition region., Comment: 13 pages, 17 figures, 3 tables

We study scaling behavior of a chiral order parameter performing a simulation of two-flavor QCD with improved Wilson quarks. It has been shown that the scaling behavior of the chiral order parameter defined by a Ward-Takahashi identity agrees with the scaling function of the three-dimensional O(4) spin model at zero chemical potential. We extend the scaling study to finite density QCD. Calculating derivatives of the chiral order parameter with respect to the chemical potential in two-flavor QCD, the scaling property of chiral phase transition is discussed in the low density region. We moreover calculate the curvature of the phase boundary of the chirl phase transition in the temperature and chemical potential plane assuming the O(4) scaling relation., Comment: 7 pages, 6 figures, poster presented at the XXVIII International Symposium on Lattice Field Theory, June 14-19 2010, Villasimius, Italy

Dirac-Sobolev and Dirac-Hardy inequalities in $L^1$ are established in which the $L^p$ spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak $L^p$ spaces. Counter examples to the analogues of the classical inequalities are shown to be provided by zero modes for appropriate Pauli operators constructed by Loss and Yau., Comment: 11 pages. To appear in Publ. RIMS, Kyoto University

We propose a new approach to finite density QCD based on a histogram method with phase quenched simulations at finite chemical potential. Integrating numerically the derivatives of the logarithm of the quark determinant with respect to the chemical potential, we calculate the reweighting factor and the complex phase of the quark determinant. The complex phase is handled with a cumulant expansion to avoid the sign problem. We examine the applicability of this method., Comment: 7 pages, 11 figures

We present the status of our study on the equation of state in 2+1 flavor QCD with non-perturbatively improved Wilson quarks coupled with the RG improved glue. We apply the T-integration method to non-perturbatively calculate the equation of state by the fixed-scale approach., Comment: 7 pages, 7 figures, talk presented at the XXVIII International Symposium on Lattice Field Theory, June 14-19 2010, Villasimius, Italy

Screening properties of the quark gluon plasma are studied from Polyakov-loop correlation in lattice QCD simulations with two flavors of improved Wilson quarks at temperatures $T/\Tpc \simeq 1$--4 where $\Tpc$ is the pseudocritical temperature. Using the Euclidean-time reflection symmetry and the charge conjugation symmetry, we introduce various types of Polyakov-loop correlation functions and extract screening masses in magnetic and electric sectors. We find that the temperature dependence of the screening masses are well described by the weak coupling expansion. We also find that a ratio of the screening masses in the electric sector to the magnetic sector shows qualitative agreement with a prediction from the dimensionally-reduced effective field theory and the N=4 supersymmetric Yang-Mills theory at $1.3 < T/\Tpc < 3$., 7 pages, 5 figures, Talk given at the XXVI International Symposium on Lattice Field Theory (LATTICE 2008), July 14-19, 2008, Williamsburg, Virginia, USA

We extend the study of the light hadron spectrum and the quark mass in two-flavor QCD to smaller sea quark mass, corresponding to $m_{PS}/m_{V}=0.60$--0.35. Numerical simulations are carried out using the RG-improved gauge action and the meanfield-improved clover quark action at $\beta=1.8$ ($a = 0.2$ fm from $\rho$ meson mass). We observe that the light hadron spectrum for small sea quark mass does not follow the expectation from chiral extrapolations with quadratic functions made from the region of $m_{PS}/m_{V}=0.80$--0.55. Whereas fits with either polynomial or continuum chiral perturbation theory (ChPT) fails, the Wilson ChPT (WChPT) that includes $a^2$ effects associated with explicit chiral symmetry breaking successfully fits the whole data: In particular, WChPT correctly predicts the light quark mass spectrum from simulations for medium heavy quark mass, such as $m_{PS}/m_V \simgt 0.5$. Reanalyzing the previous data %at $m_{PS}/m_{V}=0.80$--0.55 with the use of WChPT, we find the mean up and down quark mass being smaller than the previous result from quadratic chiral extrapolation by approximately 10%, $m_{ud}^{\bar{\rm MS}}(\mu=2 {GeV}) = 3.11(17)$ [MeV] in the continuum limit., Comment: 33 pages

We report on our study of two-flavor full QCD on anisotropic lattices using $O(a)$-improved Wilson quarks coupled with an RG-improved glue. The bare gauge and quark anisotropies corresponding to the renormalized anisotropy $\xi=a_s/a_t = 2$ are determined as functions of $\beta$ and $\kappa$, which covers the region of spatial lattice spacings $a_s\approx 0.28$--0.16 fm and $m_{PS}/m_V\approx 0.6$--0.9. The calibrations of the bare anisotropies are performed with the Wilson loop and the meson dispersion relation at 4 lattice cutoffs and 5--6 quark masses. Using the calibration results we calculate the meson mass spectrum and the Sommer scale $r_0$. We confirm that the values of $r_0$ calculated for the calibration using pseudo scalar and vector meson energy momentum dispersion relation coincide in the continuum limit within errors. This work serves to lay ground toward studies of heavy quark systems and thermodynamics of QCD including the extraction of the equation of state in the continuum limit using Wilson-type quark actions., Comment: 16 pages, 23 figures, Version accepted for publication in Physical Review D

The non-perturbative $\csw$ determined by the Schr\"{o}dinger functional (SF) method with the RG-improved gauge action in dynamical $N_f=3$ QCD shows a finite volume effect when the numerical simulations are carried out at a constant lattice size $L/a$. We remove the unwanted finite volume effect by keeping physical lattice extent $L$ at a constant. The details of the method and the result obtained for non-perturbative $\csw$ with a constant $L$ are reported., Comment: Lattice 2003 (improve), 3 pages, 3 figures

Responses to chemical potential of the pseudoscalar meson screening mass and the chiral condensate in lattice QCD are investigated. On a $16 \times 8^2 \times \4$ lattice with two flavors of staggered quarks the first and second responses below and above $T_c$ are evaluated. Different behavior in the low and the high temperature phases are observed, which may be explained as a consequence of the chiral symmetry breaking and restoration., Comment: Lattice2001(hightemp), 3pages, 3figures

We study the response of hadron masses with respect to chemical potential at $\mu=0$. Our preliminary results of the pion channel show that $\partial m/\partial \mu$ in the confinement phase is significantly larger than that in the deconfinement phase, which is consistent with the chiral restoration., Comment: LATTICE99 (finite temperature and density), 3 pages, 3 figures

We analyze temporal and spatial meson correlators in quenched lattice QCD at T>0. Above T_c we find different masses and (spatial) screening masses, signals of plasma formation, and indication of persisting mesonic excitations., 4 pages, 5 figures, revised formulation

We study the effects of the chemical potential on the $\rho$ meson mass at finite temperature. Our preliminary results show that some effects are seen in the vicinity of the phase transition point. Although the signal is still too noisy to obtain conclusive physical results within limited statistics, the mass susceptibility is consistent with zero., Comment: LATTICE98(hightemp), 3 pages

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