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Phase transitions in a fluid surface model with a deficit angle term
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EPJ manuscript No.
(will be inserted by the editor)
Phase transitions in a fluid surface model with a deficit angle
term
Hiroshi Koibuchi
Department of Mechanical and Systems Engineering
Ibaraki National College of Technology
Nakane 866, Hitachinaka, Ibaraki 312-8508, Japan
the date of receipt and acceptance should be inserted later
Abstract. Nambu-Goto model is investigated by using the canonical Monte Carlo simulation technique on
dynamically triangulated surfaces of spherical topology. We find that the model has four distinct phases;
crumpled, branched-polymer, linear, and tubular. The linear phase and the tubular phase appear to be
separated by a first-order transition. It is also found that there is no long-range two-dimensional order in
the model. In fact, no smooth surface can be seen in the whole region of the curvature modulus α, which
is the coefficient of the deficit angle term in the Hamiltonian. The bending energy, which is not included
in the Hamiltonian, remains large even at sufficiently large α in the tubular phase. On the other hand, the
surface is spontaneously compactified into a one-dimensional smooth curve in the linear phase; one of the
two degrees of freedom shrinks, and the other degree of freedom remains along the curve. Moreover, we
find that the rotational symmetry of the model is spontaneously broken in the tubular phase just as in the
same model on the fixed connectivity surfaces.
PACS. 64.60.-i General studies of phase transitions – 68.60.-p Physical properties of thin films, nonelec-
tronic – 87.16.Dg Membranes, bilayers, and vesicles
1 Introduction
Triangulated surfaces are one of the basic models to in-
vestigate the physics of biological membranes and that
of strings [1,2,3,4,5,6,7]. Surface models can exhibit a
variety of shapes because of the two-dimensional nature.
A well-known model is the one of Helfrich, Polyakov and
Kleinert (HP
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