First-order transition in a spin model for self-organization
(1999) Modern Physics Letters B : condensed matter physics; statistical physics and applied physics — Vol. 13, n° 25, p. 895-903 (1999)
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- Abstract
- The paper examines the emergence of self-organization in a population where tandem recruitment is combined with individual memory. The time evolution is modeled as a two-dimensional spin system with local interaction along the time axis and a mean-field interaction along the other axis. We generalize a previous result obtained with this model from the case of two sources to the multisource situation and show a twofold connection with the Potts model. First, when individual memory exceeds a critical value, a phase transition sets in, which is second order for two sources but first order beyond, similarly to the mean-field theory of the Potts model. In addition, the self-organization problem considered here relies on a special case of the one-dimensional nearest-neighbor Potts model with external field, which is shown to be explicitly solvable.
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Bauvin, R., & Kamp, Y. (1999). First-order transition in a spin model for self-organization. Modern Physics Letters B : condensed matter physics; statistical physics and applied physics, 13(25), 895-903. https://doi.org/10.1142/S0217984999001093 (Original work published 1999)