Phase transition of surface models with intrinsic curvature

Abstract

It is reported that a surface model of Polyakov strings undergoes a first-order phase transition between smooth and crumpled (or branched polymer) phases. The Hamiltonian of the model contains the Gaussian term and a deficit angle term corresponding to the weight of the integration measure dX in the partition function. PACS. 64.60.-i General studies of phase transitions -68.60.-p Physical properties of thin films, nonelectronic -87.16.Dg Membranes, bilayers, and vesicles

Phase transitions of a tethered membrane model with intrinsic curvature on spherical surfaces with point boundaries

“…The model was known as the one that undergoes a first-order crumpling transition without the boundary condition [39,40,41]. This paper aimed to show how boundary conditions influence the phase transition, and we performed extensive MC simulations on the spherical tethered surfaces up to a size N = 8412.…”

“…It has been shown that the first-order transition can be seen in spherical fluid/tethered surfaces [38,39], tethered surface of disk topology [40], and tethered surface with torus topology [41].…”

Monte Carlo simulations of a tethered membrane model on a disk with intrinsic curvature

“…We comment on a relation of S 3 in (1) to an intrinsic curvature energy [20]. This S 3 in [20] is intimately related with the co-ordination dependent term S 3 = − i log(q i /6), which comes from the integration measure i dX i q α i [32] in the partition function for the model on a sphere.…”

“…On the other hand, it has also been reported that there is a first-order transition in the model with Hamiltonian slightly different from the ordinary one of Helfrich and Polyakov-Kleinert on a sphere [25]. First-order transitions can also be seen in a model of Nambu-Goto Hamiltonian with a deficit angle term [26] and in a model with Hamiltonian containing the Gaussian term and an intrinsic curvature term [20]. Therefore, phase transitions of the tethered surface model should be understood more clearly.…”

“…Models on triangulated surfaces can be classified into two groups. One of them is the fluid model which is defined on dynamical connectivity surfaces [13,14,15,16,17,18,19,20], and the other is the tethered model on fixed connectivity surfaces [20,21,22,23,24,25,26,27,28,29,30]. There is another classification of surface models; a model is called real or phantom according to whether the surface is self-avoiding or not.…”