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Absence of first order transition in the random crystal field Blume-Capel model on a fully connected graph. (English) Zbl 1357.82033

Summary: We solve the Blume-Capel model on a complete graph in the presence of random crystal field with a distribution, \(P(\Delta_i)=p\delta(\Delta_i-\Delta)+(1-p)\delta(\Delta_i+\Delta)\), using large deviation techniques. We find that the first order transition of the pure system is destroyed for \(0.046<p<0.954\) for all values of the crystal field, \(\Delta\). The system has a line of continuous transition for this range of \(p\) from \(-\infty<\Delta<\infty\). For values of \(p\) outside this interval, the phase diagram of the system is similar to the pure model, with a tricritical point separating the line of first order and continuous transitions. We find that in this regime, the order vanishes for large \(\Delta\) for \(p<0.046\) (and for large \(-\Delta\) for \(p>0.954\)) even at zero temperature.

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
82B26 Phase transitions (general) in equilibrium statistical mechanics
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