Critical Behavior of Two-Dimensional Fluid 3He on a Sinusoidal Graphene

Our recent works on quasi-one dimensional and quasi-two dimensional fluid He-3 persuaded us to investigate a probable liquid -gas phase transition for the two dimensional fluid He-3 on an adsorbent substrate at finite temperature. For this purpose, we have considered a rippled graphene with a sine functional form. Here, the system thermodynamic functions have been computed by a variational approach. Our calculations for the equation of state demonstrate a liquid gas second-order phase transitions at T-c similar or equal to 0:4 K, with no external pressure, while the bulk fluid 3He requires extremely high pressure condition for a liquid -gas phase transition. Some response functions such as the compressibility and specific heat have been computed near the critical point where their divergence behaviors justify the second-order phase transition. This critical behavior of two dimensional fluid 3He on graphene disappears by ignoring the periodic ripples of substrate which shows the important role of ripples.