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Blume-Capel model

gitpages.physik.uni-wuerzburg.de · 366 words · saved by 1 readers

Simple model, rich phase diagram

The Spin-1 Blume-Capel model is a generalization of the standard Ising model with dynamics described by the Hamiltonian $$ \mathcal{H} = J\sum\limits_{\langle i,j\rangle} \phi_i\phi_j + D\sum\limits_{i} \phi_i^2, $$ where the spins take on integer values \(\phi_i=-1,0,+1\). Despite its relative simplicity, the Blume-Capel model features a rich physical phenomenology, most notably a second-order transition line, which becomes first-order for low temperatures. The second term in the Hamiltonian gives rise to a zero-field splitting , raising the energy of the \(\phi=\pm 1\) states above the \(\ph

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