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We numerically study the phase structure of two types of triangulatedspherical surface models, which includes an in-plane shear energy in theHamiltonian, and we found that the phase structure of the models isconsiderably influenced by the presence of the in-plane shear elasticity. Themodels undergo a first-order collapsing transition and a first-order (orsecond-order) transition of surface fluctuations; the latter transition wasreported to be of second-order in the first model without the in-plane shearenergy. This leads us to conclude that the in-plane elasticity strengthens thetransition of surface fluctuations. We also found that the in-plane elasticitydecreases the variety of phases in the second model without the in-planeenergy. The Hamiltonian of the first model is given by a linear combination ofthe Gaussian bond potential, a one-dimensional bending energy, and the in-planeshear energy. The second model is obtained from the first model by replacingthe Gaussian bond potential with the Nambu-Goto potential, which is defined bythe summation over the area of triangles.

Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models