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A large deviation technique is applied to the mean-field phi4-model,providing an exact expression for the configurational entropy s(v,m) as afunction of the potential energy v and the magnetization m. Although acontinuous phase transition occurs at some critical energy v_c, the entropy isfound to be a real analytic function in both arguments, and it is only themaximization over m which gives rise to a nonanalyticity in s(v)=sup_m s(v,m).This mechanism of nonanalyticity-generation by maximization over one variableof a real analytic function is restricted to systems with long-rangeinteractions and has--for continuous phase transitions--the generic occurrenceof classical critical exponents as an immediate consequence. Furthermore, thismechanism can provide an explanation why, contradictory to the so-calledtopological hypothesis, the phase transition in the mean-field phi4-model neednot be accompanied by a topology change in the family of constant-energysubmanifolds.Comment: 10 pages, 5 figure

physical review. e, statistical, nonlinear and soft matter physics

The mean-field<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>φ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>model: Entropy, analyticity, and configuration space topology

The mean-fieldφ4model: Entropy, analyticity, and configuration space topology