Hi, my name is Ofek and its my first post here. hope to be clear and if not I'll try to be more specific next time.(adsbygoogle = window.adsbygoogle || []).push({});

Link for the article: http://arxiv.org/pdf/cond-mat/9708043.pdf

Writen by N. S. Branco

The model H = J*ƩSiSj + ƩΔi(Si)^2 - first sum over nearest neighbors and second sum (i) over all lattice sites.

The distribution of Δ (crystal field) is P(Δi)= pδ(Δi + Δ)+(1-p)δ(Δi - Δ)

In the article it says that the Flow in the parameter spaceon the critical surfaceis towords the fixed point of pure (p=0) ising spin 1/2 model, the fixed point value is (p*=0,Δ*=-∞, J*=finite irrelevant constant)

I have noticed that there is another fixed point of pure ising model spin 1/2 and its on the "other side" of the Δ scale at -

- (p=1, Δ=∞, J=finite const)

My question: how can it be that with an identical (pure ising model fixed point) to the one mentioned in the article (fixed point at p=0) we got a flow from all the points on the critical surface towords the p=0 fixed point and not to the (p=1) fixed point?

(I ignored another fixed point - random fixed point that only the critical line at zero temperature flows to it, and that is because i dont think its relevant to my question)

The solution of this model (i.e. finding the critical surface and the non-trivial fixed points) is rather tedious and involves 64 renormalization equations - (recursion relation of the renormalization group).

Despite these, my main goal of writing this question here is to get an idea or proposal about the nature of this other fixed point (p=1, Δ = +∞).

If it will make things easier ill mention that at Δ=-∞ and for Δ=+∞ in the Temperature - p plane we got a Dilute spin 1/2 model (perculation) with critical p=1/2

Thanks

Ofek

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# Two dimensional Blume-Capel model with random crystal field

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