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

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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

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Dear Kruno,

"Generalized Magnetization" is different from the staggered magnetization in the frustrated models.

Please try to add the following line

BACKBONE_TYPES = 1

in your parameter file (the rhs value should be replaced by the type of J1 bonds in your lattice). This parameter tells the lattice library to ignore other bond types during detecting if the lattice is bipartite or not. "Staggeredness" (or parity of each site) will be determined based only on the backbone bonds. If the backbone network of your lattice is bipartite, "Staggered Magnetization", etc will appear in the outputs again.

Best, Synge

On 2009/11/04, at 22:52, Prsa Krunoslav wrote:

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.

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?

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

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