Folding transitions of the square-diagonal lattice |
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| Affiliation: | 1. Departamento de Física, Universidade Federal do Piauí, 57072-970, Teresina - PI, Brazil;2. Departamento de Física, Universidade Estadual do Piauí, 64002-150, Teresina - PI, Brazil;3. Campus Prof. Antonio Geovanne Alves de Sousa, Universidade Estadual do Piauí, 64260-000, Piripiri - PI, Brazil;4. Departamento de Ciências Exatas e Aplicadas, Universidade Federal de Ouro Preto, 35931-008, João Monlevade - MG, Brazil;1. School of Mathematics and Statistics, Xidian University, Xi''an, Shaanxi, 710071, People''s Republic of China;2. School of Big Data and Internet, Shenzhen Technology University, Shenzhen, Guangdong, 518118, People''s Republic of China;3. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People''s Republic of China;1. Departamento de Matemática, Universidade Federal de São Carlos, Brazil;2. Mathematical Institute, Silesian University in Opava, Na Rybníčku, 1, 74601, Opava, Czech Republic;3. Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, Avenida dos Estados, 5001, Bairro Bangu, 09.210-580, Santo André, SP - Brazil |
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| Abstract: | We address the problem of “phantom” folding of the tethered membrane modeled by the two-dimensional square lattice, with bonds on the edges and diagonals of each face. Introducing bending rigidities K1 and K2 for respectively long and short bonds, we derive the complete phase diagram of the model, using transfer matrix calculations. The latter displays two transition curves, one corresponding to a first-order (ferromagnetic) folding transition, and the other to a continuous (anti-ferromagnetic) unfolding transition. |
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