Published:
In this post I continue the discussion from this post on the ASEP and introduce the ‘Coordinate Bethe Ansatz’ approach to finding an explicit solution to the forward equation in the case of two particles. In part 1, we derived the following forward equation for the probability function of the ASEP,
Published:
A brief introduction to the asymmetric simple exclusion process (ASEP) and the forward equation for the dynamics.
Published:
In this post I continue the discussion from this post on the ASEP and introduce the ‘Coordinate Bethe Ansatz’ approach to finding an explicit solution to the forward equation in the case of two particles. In part 1, we derived the following forward equation for the probability function of the ASEP,
Published:
Here we introduce the transfer matrix of the six-vertex model and show a mathematical relationship it has with the hamiltonian of the XXZ quantum spin chain (aka Heisenberg-Ising hamiltonian). This is a follow up to my previous blog post which you can find here. The work that follows is essentially that of section 10.14 in R.J. Baxter’s book “Exactly Solved Models in Statistical Mechanics” adapted to the more specific case of the six-vertex model and XXZ spin chain (compared to the more general XYZ spin chain and eight-vertex model).
Published:
What does a model for the possible orientations of hydrogen and oxygen atoms on a sheet of ice have to do with a toy model for magnetism on a chain? Although the original aim for both of these models were describing different things, molecular structure of ice and magnetism, they are intimately related via their mathematical construction. In particular, the operators that govern the dynamics of each model commute, and thus share the same eigenvectors.
Published:
A brief introduction to the asymmetric simple exclusion process (ASEP) and the forward equation for the dynamics.
Published:
In this post I continue the discussion from this post on the ASEP and introduce the ‘Coordinate Bethe Ansatz’ approach to finding an explicit solution to the forward equation in the case of two particles. In part 1, we derived the following forward equation for the probability function of the ASEP,
Published:
Some observables from the XXZ spin-1/2 chain have shown KPZ behavior, but it is not entirely clear if the model lies within the KPZ universality class. Of particular interest for us is the one-point function, for which we aim to get an exact expression that is amenable to asymptotic analysis. This content and informal discussion is based on joint work with Axel Saenz Rodriguez.
Published:
Here we introduce the transfer matrix of the six-vertex model and show a mathematical relationship it has with the hamiltonian of the XXZ quantum spin chain (aka Heisenberg-Ising hamiltonian). This is a follow up to my previous blog post which you can find here. The work that follows is essentially that of section 10.14 in R.J. Baxter’s book “Exactly Solved Models in Statistical Mechanics” adapted to the more specific case of the six-vertex model and XXZ spin chain (compared to the more general XYZ spin chain and eight-vertex model).
Published:
What does a model for the possible orientations of hydrogen and oxygen atoms on a sheet of ice have to do with a toy model for magnetism on a chain? Although the original aim for both of these models were describing different things, molecular structure of ice and magnetism, they are intimately related via their mathematical construction. In particular, the operators that govern the dynamics of each model commute, and thus share the same eigenvectors.
Published:
A brief introduction to the asymmetric simple exclusion process (ASEP) and the forward equation for the dynamics.
Published:
Some observables from the XXZ spin-1/2 chain have shown KPZ behavior, but it is not entirely clear if the model lies within the KPZ universality class. Of particular interest for us is the one-point function, for which we aim to get an exact expression that is amenable to asymptotic analysis. This content and informal discussion is based on joint work with Axel Saenz Rodriguez.
Published:
Some observables from the XXZ spin-1/2 chain have shown KPZ behavior, but it is not entirely clear if the model lies within the KPZ universality class. Of particular interest for us is the one-point function, for which we aim to get an exact expression that is amenable to asymptotic analysis. This content and informal discussion is based on joint work with Axel Saenz Rodriguez.
Published:
Here we introduce the transfer matrix of the six-vertex model and show a mathematical relationship it has with the hamiltonian of the XXZ quantum spin chain (aka Heisenberg-Ising hamiltonian). This is a follow up to my previous blog post which you can find here. The work that follows is essentially that of section 10.14 in R.J. Baxter’s book “Exactly Solved Models in Statistical Mechanics” adapted to the more specific case of the six-vertex model and XXZ spin chain (compared to the more general XYZ spin chain and eight-vertex model).
Published:
What does a model for the possible orientations of hydrogen and oxygen atoms on a sheet of ice have to do with a toy model for magnetism on a chain? Although the original aim for both of these models were describing different things, molecular structure of ice and magnetism, they are intimately related via their mathematical construction. In particular, the operators that govern the dynamics of each model commute, and thus share the same eigenvectors.
Published:
Some observables from the XXZ spin-1/2 chain have shown KPZ behavior, but it is not entirely clear if the model lies within the KPZ universality class. Of particular interest for us is the one-point function, for which we aim to get an exact expression that is amenable to asymptotic analysis. This content and informal discussion is based on joint work with Axel Saenz Rodriguez.
Published:
Here we introduce the transfer matrix of the six-vertex model and show a mathematical relationship it has with the hamiltonian of the XXZ quantum spin chain (aka Heisenberg-Ising hamiltonian). This is a follow up to my previous blog post which you can find here. The work that follows is essentially that of section 10.14 in R.J. Baxter’s book “Exactly Solved Models in Statistical Mechanics” adapted to the more specific case of the six-vertex model and XXZ spin chain (compared to the more general XYZ spin chain and eight-vertex model).
Published:
What does a model for the possible orientations of hydrogen and oxygen atoms on a sheet of ice have to do with a toy model for magnetism on a chain? Although the original aim for both of these models were describing different things, molecular structure of ice and magnetism, they are intimately related via their mathematical construction. In particular, the operators that govern the dynamics of each model commute, and thus share the same eigenvectors.