Re: [ALPS-users] A looper question: "Binder ratio of Generalized Magnetization"==""Binder ratio of Staggered Magnetization"" for antiferromagnetic models?
Dear Fabien, thanks for your quick reply, the situation is much clearer to me now. However, I believe that without some modification of the looper code I will not be able to extract much information: The "Staggered" observables are only calculated if the lattice is explicitly bipartite. Do you know if there is there some other option/trick available? All the best and thanks! Kruno --------------------------------------------- Krunoslav Prsa, PhD student, Laboratory for neutron scattering, ETH Zurich and Paul Scherrer Institute CH-5232 Villigen-PSI, Switzerland tel:+41 56 310 20 91 --------------------------------------- Reply to: [ALPS-users] A looper question: "Binder ratio of Generalized Magnetization"==""Binder ratio of Staggered Magnetization"" for antiferromagnetic models? Dear Kruno,
Dear ALPS maintainers and users,
Thanks for your generous help and advice.
I would like to calculate the Neel temperature of a 3D antiferromagnet within the Heisenberg model using the looper application as a function of ratio of the two main interactions, J2/J1. The Binder ratio B(T) for different system dimensions L seems like the easiest way to calculate the transition temperature.
Both interactions are unfortunately antiferromagnetic, giving rise to a small frustration. The lattice is not bipartite anymore as soon as the J2 is introduced. This removes the possibility of using the staggered magnetization Ms, Ms^2, Ms^4 and the Binder ratio Bs=<Ms^4>/(<Ms^2>)^2.
If you are looking for antiferromagnetic order, the staggered magnetization is the correct order parameter (and its Binder cumulant an appropriate tool) - independently of the interactions being frustrated or not.
However, there is an additional observable still available called the "Generalized magnetization", its square, etc.
Does its Binder ratio (observable "Binder Ratio of Generalized Magnetization") correspond to the Binder ratio for staggered magnetizations for antiferromagnetic models? Does this hold if the classical ground state of the given model is, say, spiral? I.e. can I in principle use this observable to determine the order transitions for all possible models?
No - to each type of order is associated a different order parameter. The staggered magnetization is the order parameter of antiferromagnetism and therefore can locate only transitions where antiferromagnetism sets in (or out). For other orders (e.g. spiral) you must compute the corresponding order parameter. Best Fabien
I am thankful for any help you may provide.
All the best. Kruno
--------------------------------------------- Krunoslav Prsa, PhD student, Laboratory for neutron scattering, ETH Zurich and Paul Scherrer Institute CH-5232 Villigen-PSI, Switzerland tel:+41 56 310 20 91 ---------------------------------------
It should be possible but we'll have to ask Synge who wrote the looper code. Maybe I'll need to add a function to the lattice library to allow definition of staggering using a subset of bonds. One way to do it would be to explicitly do it by a basis transformation in the model. Use a staggered basis, which converts staggered magnetization to uniform magnetization, and that is always measured. Matthias On 4 Nov 2009, at 15:39, Prsa Krunoslav wrote:
Dear Fabien, thanks for your quick reply, the situation is much clearer to me now.
However, I believe that without some modification of the looper code I will not be able to extract much information: The "Staggered" observables are only calculated if the lattice is explicitly bipartite.
Do you know if there is there some other option/trick available?
All the best and thanks!
Kruno
--------------------------------------------- Krunoslav Prsa, PhD student, Laboratory for neutron scattering, ETH Zurich and Paul Scherrer Institute CH-5232 Villigen-PSI, Switzerland tel:+41 56 310 20 91 ---------------------------------------
Reply to:
[ALPS-users] A looper question: "Binder ratio of Generalized Magnetization"==""Binder ratio of Staggered Magnetization"" for antiferromagnetic models?
Dear Kruno,
Dear ALPS maintainers and users,
Thanks for your generous help and advice.
I would like to calculate the Neel temperature of a 3D antiferromagnet within the Heisenberg model using the looper application as a function of ratio of the two main interactions, J2/ J1. The Binder ratio B(T) for different system dimensions L seems like the easiest way to calculate the transition temperature.
Both interactions are unfortunately antiferromagnetic, giving rise to a small frustration. The lattice is not bipartite anymore as soon as the J2 is introduced. This removes the possibility of using the staggered magnetization Ms, Ms^2, Ms^4 and the Binder ratio Bs=<Ms^4>/(<Ms^2>)^2.
If you are looking for antiferromagnetic order, the staggered magnetization is the correct order parameter (and its Binder cumulant an appropriate tool) - independently of the interactions being frustrated or not.
However, there is an additional observable still available called the "Generalized magnetization", its square, etc.
Does its Binder ratio (observable "Binder Ratio of Generalized Magnetization") correspond to the Binder ratio for staggered magnetizations for antiferromagnetic models? Does this hold if the classical ground state of the given model is, say, spiral? I.e. can I in principle use this observable to determine the order transitions for all possible models?
No - to each type of order is associated a different order parameter. The staggered magnetization is the order parameter of antiferromagnetism and therefore can locate only transitions where antiferromagnetism sets in (or out). For other orders (e.g. spiral) you must compute the corresponding order parameter.
Best Fabien
I am thankful for any help you may provide.
All the best. Kruno
--------------------------------------------- Krunoslav Prsa, PhD student, Laboratory for neutron scattering, ETH Zurich and Paul Scherrer Institute CH-5232 Villigen-PSI, Switzerland tel:+41 56 310 20 91 ---------------------------------------
participants (2)
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Matthias Troyer
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Prsa Krunoslav