Behavior and finitesize effects of the sixth order cumulant in the threedimensional Ising universality class
Abstract
The highorder cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). This has been calculated to the sixth order in experiments. Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the threedimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at nonzero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finitesize system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finitesize effects on the temperature at which the cumulant changes sign.
Supported by Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University for Doctor (2016RC004), Major State Basic Research Development Program of China (2014CB845402) and National Natural Science Foundation of China (11405088, 11221504)
 Publication:

Chinese Physics C
 Pub Date:
 September 2016
 DOI:
 10.1088/16741137/40/9/093104
 arXiv:
 arXiv:1604.06858
 Bibcode:
 2016ChPhC..40i3104P
 Keywords:

 High Energy Physics  Lattice;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 Published version on Chinese Physics C