Fetching the paper…

Reading the bibliography…

2018

Continuum limits of sparse coupling patterns

Gubser, Steven S., Jepsen, Christian, Ji, Ziming et al.

Original
PDF
Post on X

Understand

We exhibit simple lattice systems, motivated by recently proposed cold atom experiments, whose continuum limits interpolate between real and $p$-adic smoothness as a spectral exponent is varied.

A real spatial dimension emerges in the continuum limit if the spectral exponent is negative, while a $p$-adic extra dimension emerges if the spectral exponent is positive.
We demonstrate Holder continuity conditions, both in momentum space and in position space, which quantify how smooth or ragged the two-point Green's function is as a function of the spectral exponent.
The underlying discrete dynamics of our model is defined in terms of a Gaussian partition function as a classical statistical mechanical lattice model.

Continuum limits of sparse coupling patterns · Around

Built on

F. J. Dyson, “Existence of a phase transition in a one-dimensional Ising ferromagnet,” Commun. Math. Phys
1969
Earlier work this paper cites.
P. M. Bleher and J. G. Sinai, “Investigation of the critical point in models of the type of Dyson’s hierarchical models,” Comm. Math. Phys
1973
Earlier work this paper cites.
E. Yu. Lerner and M. D. Missarov, “Scalar Models of p p -adic Quantum Field Theory and Hierarchical Models,” Theor. Math. Phys
1989
Earlier work this paper cites.

Similar

Series on Soviet and East European mathematics. World Scientific, 1994
V. Vladimirov, I. Volovich, and E. Zelenov, P-adic Analysis and Mathematical Physics · 1994
Cited alongside, same era.
Springer, 1997
F. Q. Gouvêa, p-adic Numbers · 1997
Cited alongside, same era.
P. J. Sally, “An Introduction to p p -adic Fields, Harmonic Analysis and the Representation Theory of S L ( 2 ) SL(2) ,” Letters in Mathematical Physics
1998
Cited alongside, same era.
G. Bentsen, E. Davis, and M. Schleier-Smith, private discussions
Cited in the paper.

Then

M. Missarov, “ p p -Adic Renormalization Group Solutions and the Euclidean Renormalization Group Conjectures,” P P -Adic Numbers, Ultrametric Analysis, and Applications
2012
Later among the works it cites.
C.-L. Hung, A. González-Tudela, J. I. Cirac, and H. J. Kimble, “Quantum spin dynamics with pairwise-tunable, long-range interactions,” Proceedings of the National Academy of Science
2016
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…