Geodesic
Existence and continuity of pressure in classic statistical physics
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 595-618 
R. L. Dobrushin; R. A. Minlos. Existence and continuity of pressure in classic statistical physics. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 595-618. http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a1/
@article{TVP_1967_12_4_a1,
     author = {R. L. Dobrushin and R. A. Minlos},
     title = {Existence and continuity of pressure in classic statistical physics},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {595--618},
     year = {1967},
     volume = {12},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $U(y)$ be a potential such that \begin{gather*} U(y)\ge\psi(y),\quad0\le y\le a,\quad\psi(y),\ y^r\to\infty,\quad y\to0, \\ |U(y)|\le C|y|^{-(r+\varepsilon)},\quad y>a,\quad\varepsilon>0,\quad C<\infty \end{gather*} where $\psi(y)$ is a monotone function. Let $\frac{|\Omega_N|}N\to v$, $0, where $|\Omega_N|$ is the volume of an $r$-dimensional cube $\Omega_N$, and put $$ f(v,\beta)=\lim_{N\to\infty}\frac1N\ln\int_{\Omega_N}\dots\int_{\Omega_N}\exp\biggl\{-\beta\sum_{i\ne j}U(|x_i-x_j|)\biggr\}dx_1\dots dx_N. $$ It is proved that $\frac{\partial f(v,\beta)}{\partial v}$ exists and is continuous.