title: Equivalent-neighbor Potts models in two dimensions.
abstract: We investigate the two-dimensional q=3 and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number z of equivalent neighbors. For not-too-large z, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges, the transitions become discontinuous. For q=3 we locate a tricritical point separating the continuous and discontinuous transitions near z=80, and a critical fixed point between z=8 and 12. For q=4 the transition becomes discontinuous for z>16. The scaling behavior of the q=4 model with z=16 approximates that of the q=4 merged critical-tricritical fixed point predicted by the renormalization scenario.
authors.affiliation: Lorentz Institute, Leiden University, P. O. Box 9506, 2300 RA Leiden, The Netherlands.
authors.forename: Xiaofeng
authors.initials: X
authors.lastname: Qian
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China.|State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Youjin
authors.initials: Y
authors.lastname: Deng
authors.affiliation: Physics Department, Beijing Normal University, Beijing 100875, China.
authors.forename: Yuhai
authors.initials: Y
authors.lastname: Liu
authors.affiliation: Physics Department, Beijing Normal University, Beijing 100875, China.|Beijing Computational Science Research Center, Beijing 100193, China.
authors.forename: Wenan
authors.initials: W
authors.lastname: Guo
authors.affiliation: Lorentz Institute, Leiden University, P. O. Box 9506, 2300 RA Leiden, The Netherlands.
authors.forename: Henk W J
authors.initials: HW
authors.lastname: Blöte