TY - CHAP
T1 - One-Dimensional Lattice Gas with Exponential Attractive Potentials
AU - Pirjol, Dan
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - This chapter considers the Kac-Helfand system: an one-dimensional lattice gas with n sites and exponential attractive interaction εij= - αγe- γ | i - j |. The solution of this system is derived, in the grand canonical ensemble, taking the thermodynamical limit n→ ∞ at fixed ratio of the interaction range to the lattice size γ- 1/ n= 1 / a. The existence of a phase transition at finite a is demonstrated explicitly. The solution reduces to the van der Waals theory in the limit a→ ∞.
AB - This chapter considers the Kac-Helfand system: an one-dimensional lattice gas with n sites and exponential attractive interaction εij= - αγe- γ | i - j |. The solution of this system is derived, in the grand canonical ensemble, taking the thermodynamical limit n→ ∞ at fixed ratio of the interaction range to the lattice size γ- 1/ n= 1 / a. The existence of a phase transition at finite a is demonstrated explicitly. The solution reduces to the van der Waals theory in the limit a→ ∞.
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U2 - 10.1007/978-3-031-11143-3_5
DO - 10.1007/978-3-031-11143-3_5
M3 - Chapter
AN - SCOPUS:85137544401
T3 - SpringerBriefs in Applied Sciences and Technology
SP - 77
EP - 95
BT - SpringerBriefs in Applied Sciences and Technology
ER -