Related papers: Nambu and the Ising Model
The years of 1960-1965 were a remarkable period for Yoichiro Nambu. Starting with a reformulation of BCS theory with emphasis on gauge invariance, he recognized the realization of spontaneous chiral symmetry breaking in particle physics as…
We take the occasion of this article to review one hundred years of the physical and mathematical study of the Ising model. The model, introduced by Lenz in 1920, has been at the cornerstone of many major revolutions in statistical…
The Ising model is one of the standard models in statistical physics. Since 1969 more than 12000 publications appeared using this model. In 1996 Ernst Ising celebrated his 96th birthday. Some biographical notes and milestones of the…
A Local Resolution of the Problem of Time has recently been given, alongside reformulation as A Local Theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in…
In this note, I recollect a two-week period in September 1968 when I factorized the Veneziano model using string variables in Chicago. Professor Yoichiro Nambu went on to calculate the N-particle dual resonance model and then to factorize…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
Some years ago Mosh\'e Flato pointed up that it could be interesting to develop the Nambu's idea to generalize Hamiltonian mechanic. An interesting new formalism in that direction was proposed by T. Takhtajan. His theory gave new…
The exact solution of the two-dimensional Ising model by Onsager in 1944 represents one of the landmarks in theoretical physics. On the occassion of the fifty years of the exact solution, we give a historical review of this model. After…
We develop a Hamilton-Jacobi-like formulation of Nambu mechanics. The Nambu mechanics, originally proposed by Nambu more than four decades ago, provides a remarkable extension of the standard Hamilton equations of motion in even dimensional…
The life of Ernst Ising and the steps to solving the model named after him are reported in parallel. Wilhelm Lenz suggested his student Ernst Ising to explain the existence of ferromagnetism on the basis of his publication in 1920. The…
Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is…
The classical and quantum features of Nambu mechanics are analyzed and fundamental issues are resolved. The classical theory is reviewed and developed utilizing varied examples. The quantum theory is discussed in a parallel presentation,…
Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is a deformation of canonical Quantum Mechanics in which only the time-evolution of the "phases" of energy eigenstates is modified. We discuss the effect this theory will…
This paper is based on a talk delivered on 16 November, 2015 in Osaka at the Nambu's Century: International Symposium on Yoichiro Nambu's Physics
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
This is a biographical sketch and tribute to Abraham Robinson (1918-1974) on the 95th anniversary of his birth with a short discussion of the place of nonstandard analysis in the present-day mathematics.
As Basu (1977) writes, "Eliminating nuisance parameters from a model is universally recognized as a major problem of statistics," but after more than 50 years since Basu wrote these words, the two mainstream schools of thought in statistics…
A major result of the Effective String Theory (EST) description of confinement is the so called "low energy universality," which states that the first few terms of the large distance expansion of any EST are universal and coincide with…
Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample…
We show that the NP-hard quadratic unconstrained binary optimization (QUBO) problem on a graph $G$ can be solved using an adiabatic quantum computer that implements an Ising spin-1/2 Hamiltonian, by reduction through minor-embedding of $G$…