Cusp singularity in mean field Ising model

@article{Abe2017CuspSI,
  title={Cusp singularity in mean field Ising model},
  author={Yayoi Abe and M. Ishida and Erika Nozawa and T. Ootsuka and R. Yahagi},
  journal={arXiv: Mathematical Physics},
  year={2017}
}
An entropy of the Ising model in the mean field approximation is derived by the Hamilton-Jacobi formalism. We consider a grand canonical ensemble with respect to the temperature and the external magnetic field. A cusp arises at the critical point, which shows a simple and new geometrical aspect of this model. In educational sense, this curve with a cusp helps students acquire a more intuitive view on statistical phase transitions. 
1 Citations

Figures from this paper

The polarization within and across individuals: the hierarchical Ising opinion model
TLDR
This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate. Expand

References

SHOWING 1-10 OF 14 REFERENCES
Riemannian geometry in thermodynamic fluctuation theory
Although thermodynamic fluctuation theory originated from statistical mechanics, it may be put on a completely thermodynamic basis, in no essential need of any microscopic foundation. This reviewExpand
Geometrical structure of the state space in classical statistical and phenomenological thermodynamics
Abstract A unified statistical and phenomenological approach to geometrization of classical thermodynamics is proposed. It is shown that any r -parameter probability distribution function leads to aExpand
Energy-momentum conservation laws in Finsler/Kawaguchi Lagrangian formulation
We reformulate the standard Lagrangian formulation to a reparameterization invariant Lagrangian formulation by means of Finsler and Kawaguchi geometry. In our formulation, various types of symmetriesExpand
An Introduction to Riemann-Finsler Geometry
One Finsler Manifolds and Their Curvature.- 1 Finsler Manifolds and the Fundamentals of Minkowski Norms.- 1.0 Physical Motivations.- 1.1 Finsler Structures: Definitions and Conventions.- 1.2 TwoExpand
Caratheodory-Hamilton-Jacobi theory in optimal control.
Abstract In this paper we have presented the Caratheodory approach to the calculus of Variations as modified to suit optimal control problems. This method is by determining and solving a problemExpand
Topology from the differentiable viewpoint
Preface1Smooth manifolds and smooth maps1Tangent spaces and derivatives2Regular values7The fundamental theorem of algebra82The theorem of Sard and Brown10Manifolds with boundary12The Brouwer fixedExpand
Geometry
• Use a scale or scale factor to find a measurement. • Find actual lengths and areas from a scale drawing, using a scale factor. • Create multiple scale drawings from the original model or drawing,Expand
Finsler geometry in classical physics
  • J. College Arts Scie. Chiba Univ. 2, 12-16
  • 1956
Finsler structure in thermodynamics and statistical mechanics
  • AMAPN 26, 377- 382
  • 2010
Singularity Theory and Its Application
...
1
2
...