Related papers: Free energy in the Sherrington-Kirkpatrick model w…
This paper has been withdrawn.
We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures $\beta>0$. To characterize the free energy,…
This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.
This paper has been withdrawn by the author.
We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given by a variational formula involving the…
This paper has been withdrawn by the authors
This paper has been withdrawn.
This paper was withdrawn by the author. It turns out that similar ideas have been presented before. The author apologizes.
We prove the convergence in distribution of the fluctuations of the free energy of the mixed $p$-spin Sherrington-Kirkpatrick model with non-vanishing $2$-spin component at high enough temperature. The limit is Gaussian, and the…
This paper has been withdrawn by the authors, since the reference citation were not appropriately arranged.
This paper has been withdrawn by the author due to error in equation (46).
This paper has been withdrawn by the author due to the appearence of enlarged version with one new author name more (hep-ph/0012293).
The paper is withdrawn by the author due to a recently discovered flaw in a basic proof.
This paper has been withdrawn by the authors in order to replace it with a more correct treatment. The basic results remain the same but the treatment is more rigorously correct.
This paper has been withdrawn by the author.
This paper has been withdrawn
The paper has been withdrawn
This paper has been withdrawn to address an omission. It will be resubmitted in the near future.
This paper has been withdrawn by the author.
This paper has been withdrawn due to non-clearness of some technical points, as well as lack of a reasonable statement of quantization conjecture.