Effects of finite volume and magnetic fields on thermodynamic properties of quark matter and fluctuations of conserved charges

In the current work, we present the influence of finite volume and magnetic field on the thermodynamic properties of isospin asymmetric quark matter using the Polyakov loop extended chiral SU(3) quark mean field (PCQMF) model at finite chemical potential and temperature. Within the PCQMF model, we use the scalar and vector field values in mean-field approximation to obtain the thermodynamic properties: pressure density, entropy density, and energy density. The susceptibilities of conserved charges for strongly interacting matter for different system sizes as well as for different values of the magnetic field have been studied. A sizable shift in phase boundary towards the higher values of quark chemical potential (${\mu }_q$) and temperature ($T$) has been observed for decreasing values of system volume as well as an opposite shift towards lower temperature and quark chemical potential for increasing magnetic field. We observe an enhancement in fluctuations of conserved charges in the regime of the transition temperature. These studies may have a significant role in understanding the thermodynamic observables extracted from heavy-ion collisions data.

Figure 1

The scalar fields $\sigma$, $\zeta$, $\delta$, and $\chi$ are shown as a function of temperature $T$, for magnetic field $eB=0$, 0.1, 0.2, and 0.4 ${\mathrm{GeV}}^2$ and length of cubic volum $R=\infty$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 1

The scalar fields $\sigma$, $\zeta$, $\delta$, and $\chi$ are shown as a function of temperature $T$, for magnetic field $eB=0$, 0.1, 0.2, and 0.4 ${\mathrm{GeV}}^2$ and length of cubic volum $R=\infty$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 2

The Polyakov loop fields, $\mathrm{\Phi }$ and $\overline{\mathrm{\Phi }}$ shown as a function of temperature $T$, for magnetic field $eB=0$, 0.1, 0.2, and 0.4 ${\mathrm{GeV}}^2$ and length of cubic volume $R=\infty$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 2

The Polyakov loop fields, $\mathrm{\Phi }$ and $\overline{\mathrm{\Phi }}$ shown as a function of temperature $T$, for magnetic field $eB=0$, 0.1, 0.2, and 0.4 ${\mathrm{GeV}}^2$ and length of cubic volume $R=\infty$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 3

The scalar fields $\sigma$, $\zeta$, $\delta$, and $\chi$ shown as a function of temperature $T$, for length of cubic volume $R=\infty$, 5, 4, and 2 fm and magnetic field $eB=0$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 3

The scalar fields $\sigma$, $\zeta$, $\delta$, and $\chi$ shown as a function of temperature $T$, for length of cubic volume $R=\infty$, 5, 4, and 2 fm and magnetic field $eB=0$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 4

The Polyakov loop fields, $\mathrm{\Phi }$ and $\overline{\mathrm{\Phi }}$ shown as a function of temperature $T$, for length of cubic volume, $R=\infty$, 5, 4, and 2 fm and magnetic field $eB=0$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential, ${\mu }_S=200\mathrm{MeV}$.

Figure 4

The Polyakov loop fields, $\mathrm{\Phi }$ and $\overline{\mathrm{\Phi }}$ shown as a function of temperature $T$, for length of cubic volume, $R=\infty$, 5, 4, and 2 fm and magnetic field $eB=0$, baryonic chemical potential ${\mu }_B=0$ and 200 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential, ${\mu }_S=200\mathrm{MeV}$.

Figure 5

The effective quark masses $m_u^{*}$, $m_d^{*}$, and $m_s^{*}$ shown as a function of temperature $T$, for different values of length of cubic volume ($R$) and magnetic field ($eB$), baryonic chemical potential fixed at ${\mu }_B=200\mathrm{MeV}$, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 5

The effective quark masses $m_u^{*}$, $m_d^{*}$, and $m_s^{*}$ shown as a function of temperature $T$, for different values of length of cubic volume ($R$) and magnetic field ($eB$), baryonic chemical potential fixed at ${\mu }_B=200\mathrm{MeV}$, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 6

The pressure density $p$, entropy density $s$, trace anomaly ($\epsilon \text{−}3p)/T^4$, and energy density $\epsilon$ as a function of temperature for different values of length of cubic volume ($R$) and magnetic field ($eB$) at baryonic chemical potential ${\mu }_B=200\mathrm{MeV}$, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 6

The pressure density $p$, entropy density $s$, trace anomaly ($\epsilon \text{−}3p)/T^4$, and energy density $\epsilon$ as a function of temperature for different values of length of cubic volume ($R$) and magnetic field ($eB$) at baryonic chemical potential ${\mu }_B=200\mathrm{MeV}$, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 7

The derivative of scalar field $\sigma$ and Polyakov loop field, $\mathrm{\Phi }$ shown as a function of temperature $T$, varying values of length of cubic volume $R$, and magnetic field $eB$. The baryonic chemical potential ${\mu }_B=0$, 200, 400, 600 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 7

The derivative of scalar field $\sigma$ and Polyakov loop field, $\mathrm{\Phi }$ shown as a function of temperature $T$, varying values of length of cubic volume $R$, and magnetic field $eB$. The baryonic chemical potential ${\mu }_B=0$, 200, 400, 600 MeV, isospin chemical potential ${\mu }_I=80\mathrm{MeV}$, and strangeness chemical potential ${\mu }_S=200\mathrm{MeV}$.

Figure 8

The derivative of strange scalar field $\zeta$ shown as a function of temperature $T$ for ${\mu }_q=0$, 350 MeV at varying values of length of cubic volume $R$ and magnetic field $eB$.

Figure 8

The derivative of strange scalar field $\zeta$ shown as a function of temperature $T$ for ${\mu }_q=0$, 350 MeV at varying values of length of cubic volume $R$ and magnetic field $eB$.

Figure 9

In the above panel, the $T-{\mu }_q$ phase diagram for $eB=0$, 0.1, 0.2, and 0.4 ${\mathrm{GeV}}^2$ at infinite value of length of cubic volume ($R$) has been plotted. In the below panel, we show the phase diagram for various cubic length $R=\infty$, 5, 4, and 2 fm and zero value of magnetic field ($eB$).

Figure 10

The second order baryon number susceptibility (${\chi }_2^B$) and fourth order baryon number susceptibility (${\chi }_4^B$) as a function of temperature for varying value of system size ($R$) and magnetic field ($eB$). The data has been compared with lattice data.

Figure 11

The kurtosis (${\chi }_4^B/{\chi }_2^B$) and sixth order baryon number susceptibility (${\chi }_6^B$) as a function of temperature for varying value of system size ($R$) and magnetic field ($eB$). The data have been compared with lattice data.

Figure 12

The second order strangeness number susceptibility (${\chi }_2^S$) and fourth order strangeness number susceptibility (${\chi }_4^S$) as a function of temperature for varying value of system size ($R$) and magnetic field ($eB$). The data have been compared with lattice data.

Figure 13

The kurtosis (${\chi }_4^S/{\chi }_2^S$) and sixth order strangeness number susceptibility (${\chi }_6^S$) as a function of temperature for varying value of system size ($R$) and magnetic field ($eB$).

Figure 14

The second order charge number susceptibility (${\chi }_2^Q$) and fourth order charge number susceptibility (${\chi }_4^q$) as a function of temperature for varying values of system size ($R$) and magnetic field ($eB$). The data have been compared with lattice data.

Figure 15

The kurtosis (${\chi }_4^Q/{\chi }_2^Q$) and sixth order charge number susceptibility (${\chi }_6^Q$) as a function of temperature for varying value of system size ($R$) and magnetic field ($eB$).