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Long-Range Critical Exponents near the Short-Range Crossover.

Connor Behan¹, Leonardo Rastelli¹, Slava Rychkov^2,3

¹C. N. Yang Institute for Theoretical Physics, SUNY, Stony Brook, New York 11794-3840, USA.

Physical Review Letters

|July 1, 2017

Summary

This summary is machine-generated.

Researchers explored the long-range Ising model, finding a new, weakly coupled description near crossover points. This offers a novel infrared duality and precise critical exponent calculations.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics
Quantum Field Theory

Background:

The d-dimensional long-range Ising model features spin-spin interactions decaying as 1/r^{d+s}.
It exhibits a second-order phase transition with continuously varying critical exponents.
A crossover to the short-range universality class occurs at s=s_{*}.

Purpose of the Study:

To find a new, weakly coupled field-theoretic description for the long-range Ising model near the crossover.
To compute critical exponents using this new description.
To demonstrate a novel example of infrared duality.

Main Methods:

Utilized a novel field-theoretic description that is weakly coupled near the crossover.
Applied this description to calculate critical exponents of the model.
Investigated the complementary ultraviolet (UV) descriptions of the long-range fixed point.

Main Results:

A new, weakly coupled description for the long-range Ising model near the crossover was successfully developed.
Critical exponents were computed with enhanced precision using this new formulation.
The study revealed two complementary UV descriptions for the same long-range fixed point.

Conclusions:

The newly found weakly coupled description provides a powerful tool for studying the long-range Ising model.
The existence of two complementary UV descriptions highlights a novel instance of infrared duality.
This work advances the understanding of critical phenomena in systems with long-range interactions.