Thermodynamic curvature for a two-parameter spin model with frustration

Abstract

Microscopic models of realistic thermodynamic systems usually involve a number of parameters, not all of equal macroscopic relevance. We examine a decorated $(1+3)$ Ising spin chain containing two microscopic parameters: a "stiff" $K$ mediating the long-range interactions, and a "sloppy" $J$ operating within local spin groups. $K$ dominates the macroscopic behavior, and varying $J$ has weak effect except in regions where $J$ brings about transitions between phases through its conditioning of the local spin groups with which $K$ interacts. We calculate the heat capacity $C_H$, the magnetic susceptibility ${\chi }_T$, and the thermodynamic curvature $R$. For large $|J/K|$, we identify four magnetic phases: ferromagnetic, antiferromagnetic, and two ferrimagnetic ones, according to the signs of $K$ and $J$. We argue that for characterizing these phases, the strongest picture is offered by the thermodynamic geometric invariant $R$, proportional to the correlation length $\xi$. This picture has correspondences to other cases, such as fluids.

13 pages, 4 figures, 25 references

References in corpus (12)

• Parameter Space Compression Underlies Emergent Theories and Predictive Models
• The sloppy model universality class and the Vandermonde matrix
• Thermodynamic curvature measures interactions
• Information geometry in vapour-liquid equilibrium
• Thermodynamic curvature from the critical point to the triple point
• Exactly solvable Ising--Heisenberg chain with triangular XXZ-Heisenberg plaquettes
• The Information Geometry of the One-Dimensional Potts Model
• The Information Geometry of the Ising Model on Planar Random Graphs
• Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds
• Phase diagram of a coupled tetrahedral Heisenberg model
• Thermodynamic geometry of a kagome Ising model in a magnetic field
• Stability and anyonic behavior of systems with M-statistics

Cited by in corpus (7)

• Thermodynamic curvature of the binary van der Waals fluid
• Thermodynamic metric geometry of the two-state ST2 model for supercooled water
• Fluctuations and thermodynamic geometry of the chiral phase transition
• Thermodynamic Geometry of the Quark-Meson Model
• Geometrical aspects of the multicritical phase diagrams for the Blume-Emery-Griffiths model
• Geometric Thermodynamics of Strain-Induced Crystallization in Polymers
• Information-Geometric Signatures from Nonextensivity in the $1$-D Blume-Capel Model