Author(s):
1. Milan Pantić, Univerzitet u Novom Sadu, Prirodno-matematički fakultet, Departman za fiziku, Serbia

Abstract:
In this work, a one-dimensional generalized Ising model on a monoatomic, equidistant lattice is analyzed, considering various interactions between spins of first and further neighbors. The Kramers–Wannier transfer matrix with double lattice translation is derived, enabling precise determination of the system’s ground state. Phase diagrams encompassing all types of magnetic ordering are constructed, revealing a large number of triple points and lines of phase coexistence, in full agreement with Gibbs' phase rule. An effect analogous to overheating/underheating is observed, while phases at triple points are frustrated, indicating the occurrence of critical opalescence. Exact analytical expressions are derived for the Gibbs free energy, internal energy, heat capacity, and entropy, including the entropy at absolute zero. The results are compared with existing data, including those for two-dimensional lattices.

Key words:
Ising model,one-dimensional lattice,Kramers–Wannier transfer matrix,phase diagrams,triple points,Gibbs free energy,critical opalescence,heat capacity,entropy,magnetic ordering

Thematic field:
SYMPOSIUM A - Science of matter, condensed matter and physics of solid states

Date of abstract submission:
16.07.2025.

Conference:
Contemporary Materials 2025 - Savremeni Materijali