The Romance of the Ising Model

McCoy, Barry M.

doi:10.1007/978-1-4471-4863-0_11

Cited by 4 publications

(2 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For technical details and historical context, see refs. [1][2][3][4][5][6][7][8][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

mentioning

confidence: 99%

See 1 more Smart Citation

The hypergeometric series for the partition function of the 2D Ising model

Viswanathan¹

2015

J. Stat. Mech.

View full text Add to dashboard Cite

Abstract. In 1944 Onsager published the formula for the partition function of the Ising model for the infinite square lattice. He was able to express the internal energy in terms of a special function, but he left the free energy as a definite integral. Seven decades later, the partition function and free energy have yet to be written in closed form, even with the aid of special functions. Here we evaluate the definite integral explicitly, using hypergeometric series. Let β denote the reciprocal temperature, J the coupling and f the free energy per spin. We prove that −βf = ln(2 cosh 2K) −

show abstract

“…For technical details and historical context, see refs. [1][2][3][4][5][6][7][8][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

mentioning

confidence: 99%

“…and versions of expressions ( 4) and ( 6) are those found in the textbooks. For technical details and historical context, see [1][2][3][4][5][6][7][8][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

mentioning

confidence: 99%

The hypergeometric series for the partition function of the 2D Ising model

Viswanathan¹

2015

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

The Ising magnetization exponent on $$\mathbb{Z }^2$$ is $$1/15$$

Camia

Garban

Newman

2013

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

We prove that for the Ising model defined on the plane Z 2 at β = β c , the average magnetization under an external magnetic field h > 0 behaves exactly likeThe proof, which is surprisingly simple compared to an analogous result for percolation (i.e. that θ(p) = (p − p c ) 5/36+o(1) on the triangular lattice [SmW01, K87]) relies on the GHS inequality as well as the RSW theorem for FK percolation from [DHN11]. The use of GHS to obtain inequalities involving critical exponents is not new; in this paper we show how it can be combined with RSW to obtain matching upper and lower bounds for the average magnetization.

show abstract

An operator theoretic approach to the brickwork Ising model with second-neighbor interactions

Böttcher

2013

Linear Algebra and its Applications

View full text Add to dashboard Cite

The Romance of the Ising Model

Cited by 4 publications

References 72 publications

The hypergeometric series for the partition function of the 2D Ising model

The hypergeometric series for the partition function of the 2D Ising model

The Ising magnetization exponent on $$\mathbb{Z }^2$$ is $$1/15$$

An operator theoretic approach to the brickwork Ising model with second-neighbor interactions

Contact Info

Product

Resources

About