Finite dt dependence of the Binder cumulants for 3-flavor QCD at finite temperature and isospin density

Abstract

We simulate 3-flavour lattice QCD at small isospin chemical potential ${\mu }_I$ and finite temperature $T$. At ${\mu }_I=0$ there is a critical mass $m_c$ where the finite-temperature transition changes from first order to a crossover. We measure the ${\mu }_I$ dependence of the transition $\beta$ (${\beta }_c$) for $m$ close to $m_c$. ${\beta }_c$ and hence $T_c$ decrease slowly with increasing ${\mu }_I$. ${\beta }_c$ at finite ${\mu }_I$ is in good agreement ${\beta }_c$ at finite $\mu$ (quark-number chemical potential). We use fourth-order Binder cumulants to determine the nature of this transition and to search for a critical endpoint. We measure the $dt$ dependence of these cumulants and extrapolate to $dt=0$. ($dt$ is the `time' increment used in the hybrid molecular-dynamics simulations.) Preliminary measurements of these Binder cumulants show little ${\mu }_I$ dependence. (Simulations at imaginary $\mu$ indicate that the $\mu$ dependence of the Binder cumulants is also weak.) This contrasts to the ${\mu }_I$ dependence we observed at fixed $dt$.

15 pages, 6 figures. Talk presented at the Workshop on QCD in Extreme Environments, Argonne National Laboratory, 29th June to 3rd July, 2004

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