Transfer matrix in statistical mechanics - 편집 역사

2020년 12월 28일 (월) 12:07에 Pythagoras0님의 편집

2020-12-28T12:07:25Z

2020-11-16T17:49:48Z

2020-11-13T10:04:56Z

2020-11-13T10:04:56Z

2013-06-30T13:19:26Z

expositions

2013-04-10T09:43:22Z

2013-02-19T21:10:59Z

2013-02-19T21:07:39Z

2013-02-19T20:56:44Z

2013-02-04T11:18:19Z

정의

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
-* transfer matrix is builtup from matrices of  Boltzmann weights
+* transfer matrix is builtup from matrices of  Boltzmann weights
 * trace of [[Monodromy matrix]] is the transfer matrix
 * finding eigenvalues and eigenvectors of transfer matrix is crucial
-* partition function = trace of power of transfer matrices
+* partition function = trace of power of transfer matrices
-* so the partition function  is calculated in terms of the eigenvalues of the transfer matrix
+* so the partition function  is calculated in terms of the eigenvalues of the transfer matrix
 * then the problem of solving the model is reduced to the computation of this trace
@@ 15번째 줄: / 15번째 줄: @@
 * [[Six-vertex model and Quantum XXZ Hamiltonian]]
-−
 ==related items==

← 이전 판	2020년 11월 13일 (금) 10:04 판
1번째 줄:	1번째 줄:
	+	==introduction==
	+	* transfer matrix is builtup from matrices of Boltzmann weights
	+	* trace of [[Monodromy matrix]] is the transfer matrix
	+	* finding eigenvalues and eigenvectors of transfer matrix is crucial
	+	* partition function = trace of power of transfer matrices
	+	* so the partition function is calculated in terms of the eigenvalues of the transfer matrix
	+	* then the problem of solving the model is reduced to the computation of this trace

	+
	+	==Bethe ansatz==
	+	* [[Bethe ansatz]] equation is used to find the eigenvectors and eigenvalues of the transfer matrix
	+
	+
	+	==transfer matrix of the six-vertex model==
	+	* [[Six-vertex model and Quantum XXZ Hamiltonian]]
	+
	+
	+
	+	==related items==
	+	* [[S-matrix or scattering matrix]]
	+	* [[1d Ising model]]
	+	* [[Ising model on rectangular lattice]]
	+
	+
	+
	+	==expositions==
	+	* “The Kramers-Wannier Transfer Matrix.” 1980. In The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics, 13–39. Lecture Notes in Physics 123. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0017921.
	+	[[분류:개인노트]]
	+	[[분류:integrable systems]]
	+	[[분류:math and physics]]
	+	[[분류:migrate]]

← 이전 판		2020년 11월 13일 (금) 10:04 판
1번째 줄:		1번째 줄:
−	~~==introduction==~~
−	* transfer matrix is builtup from matrices of Boltzmann weights
−	* trace of [[Monodromy matrix]] is the transfer matrix
−	* finding eigenvalues and eigenvectors of transfer matrix is crucial
−	* partition function = trace of power of transfer matrices
−	* so the partition function is calculated in terms of the eigenvalues of the transfer matrix
−	* then the problem of solving the model is reduced to the computation of this trace

−
−	~~==Bethe ansatz==~~
−	* [[Bethe ansatz]] equation is used to find the eigenvectors and eigenvalues of the transfer matrix
−
−
−	~~==transfer matrix of the six-vertex model==~~
−	* [[Six-vertex model and Quantum XXZ Hamiltonian]]
−
−
−
−	~~==related items==~~
−	* [[S-matrix or scattering matrix]]
−	* [[1d Ising model]]
−	* [[Ising model on rectangular lattice]]
−
−
−
−	~~==expositions==~~
−	* “The Kramers-Wannier Transfer Matrix.” 1980. In The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics, 13–39. Lecture Notes in Physics 123. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0017921.
−	~~[[분류:개인노트]]~~
−	~~[[분류:integrable systems]]~~
−	~~[[분류:math and physics]]~~

@@ 25번째 줄: / 25번째 줄: @@
 ==expositions==
+* “The Kramers-Wannier Transfer Matrix.” 1980. In The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics, 13–39. Lecture Notes in Physics 123. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0017921.
 [[분류:개인노트]]
 [[분류:integrable systems]]
 [[분류:math and physics]]

@@ 1번째 줄: / 1번째 줄: @@
 ==introduction==
 * transfer matrix is builtup from matrices of  Boltzmann weights
-* trace of monodromy matrix is the transfer matrix
+* trace of [[Monodromy matrix]] is the transfer matrix
 * finding eigenvalues and eigenvectors of transfer matrix is crucial
 * partition function = trace of power of transfer matrices

← 이전 판	2020년 11월 16일 (월) 17:49 판
(차이 없음)

@@ 3번째 줄: / 3번째 줄: @@
 * trace of monodromy matrix is the transfer matrix
 * finding eigenvalues and eigenvectors of transfer matrix is crucial
 * partition function = trace of power of transfer matrices
 * so the partition function  is calculated in terms of the eigenvalues of the transfer matrix
@@ 9번째 줄: / 8번째 줄: @@
-==transfer matrix of the 1D Ising model==
+==Bethe ansatz==
-* [[1d Ising model]]
+* [[Bethe ansatz]] equation is used to find the eigenvectors and eigenvalues of the transfer matrix
@@ 25번째 줄: / 19번째 줄: @@
 ==related items==
 * [[S-matrix or scattering matrix]]
 ==expositions==

@@ 19번째 줄: / 19번째 줄: @@
 * 자유에너지(per site) 는 다음과 같다
 $$
-f=-\frac{1}{\beta}\lim_{N\to \infty}\frac{\ln \Lambda_0^N}{N}=-\frac{1}{\beta}\ln \Lambda_0
+F=-\frac{1}{\beta}\lim_{N\to \infty}\frac{\ln \Lambda_0^N}{N}=-\frac{1}{\beta}\ln \Lambda_0,
 $$
 이 때 $\Lambda_0$는 $T$의 최대인 고유값