Buldyrev and Stanley model

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The Buldyrev and Stanley model consists of a double shoulder plus a square well (Ref. 1 Eq. 1):

\Phi_{12}\left( r \right) = 
\left\{ \begin{array}{ccc}
\infty & ; & r < a \\
U_1 & ; &a \le r < b_1 \\
U_2 & ; & b_1 \le r < b_2 \\
-U_A & ; & b_2 \le r < c \\
0         & ; & r \ge c \end{array} \right.

where \Phi_{12} (r) is the intermolecular pair potential, r := |\mathbf{r}_1 - \mathbf{r}_2|, and c>b_2>b_1>a and U_A>0.


  1. Sergey V. Buldyrev and H. Eugene Stanley "A system with multiple liquid–liquid critical points", Physica A 330 pp. 124-129 (2003)