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Multiple phase changes induced by frustration in randomly connected cellular automata

Normand Mousseau

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Frustration is introduced in randomly connected totalistic cellular automata via mixing rules leading to incompatible periods. As the respective concentration of rules is varied, these cellular automata go through eight phases, many of which with symmetries different from the two rules mixed in. The complex phase diagram so created is similar to those seen in frustrated systems in static equilibrium. It shows that a minimized free energy is not necessary for frustration to produce this rich behaviour.


PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects

75.10.Nr Spin-glass and other random models

05.70.Ce Thermodynamic functions and equations of state

MSC

37B15 Cellular automata

68Q80 Cellular automata (See also 37B15)

82B26 Phase transitions (general)

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82D40 Magnetic materials

Subjects

Condensed matter: electrical, magnetic and optical

Statistical physics and nonlinear systems

Dates

Issue 9 (7 May 1997)

Received 9 September 1996, in final form 6 December 1996



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