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 $dt$.