Direct SpinSusceptibility?

[evanberkowitz]

In the worldline the spin susceptibility is quite involved. You've first got to compute the costly Spin_Spin correlator and then sum it up. Is there some more clever approach where we can sum over x and y first?

[evanberkowitz]

In 'normal' lattice calculations might compute eg. < φ† φ >, rather than what we have, exp(i ∆φ). The way we might do it is by computing the (gauge-field-dependent) propagator.

So for example in the Villain formulation we can expand (dφ–2πn)^2 = (dφ)^2 + 2 dφ n + n^2. Integrating by parts we get –φ δd φ – 2 φ δn + n^2. Then we could in principle calculate correlations of φ by performing inversions (since φ and n have linear mixing, presumably we need to solve an annoying matrix).

But I'm not sure what to do for the correlator we've actually got, < exp{+iφ} exp{–iφ} >. How can we use the solved propagator to get the exponential of the operator rather than the operator downstairs?

[evanberkowitz]

I'm closing this as we now understand how to measure the < exp{+iφ} exp{–iφ} > correlator using the worm.

It may still be interesting to attempt to formulate the φ propagator via a linear solve and use it for observables, but so far no need.