# Conformal symmetry of the critical 3D Ising model inside a sphere

@article{Cosme2015ConformalSO, title={Conformal symmetry of the critical 3D Ising model inside a sphere}, author={Catarina Martins Cosme and J. Viana Lopes and Jo{\~a}o Penedones}, journal={Journal of High Energy Physics}, year={2015}, volume={2015}, pages={1-15} }

A bstractWe perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.

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#### References

SHOWING 1-10 OF 35 REFERENCES

Solving the 3D Ising Model with the Conformal Bootstrap

- Physics
- 2012

We study the constraints of crossing symmetry and unitarity in general 3D conformal field theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars… Expand

Bulk and surface critical behavior of the three-dimensional Ising model and conformal invariance.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

The precision of these results reveals that, as in two dimensions, conformal mappings provide a powerful tool to investigate critical phenomena and confirms that the critical three-dimensional Ising model is conformally invariant. Expand

Line defects in the 3d Ising model

- Physics
- 2013

A bstractWe investigate the properties of the twist line defect in the critical 3d Ising model using Monte Carlo simulations. In this model the twist line defect is the boundary of a surface of… Expand

Monte Carlo simulations of conformal theory predictions for the three-state Potts model

- Physics, Mathematics
- 1996

The critical properties of the three-state Potts model are investigated using Monte Carlo simulations. Special interest is given to the measurement of three-point correlation functions and associated… Expand

Boundary and interface CFTs from the conformal bootstrap

- Physics
- 2015

A bstractWe explore some consequences of the crossing symmetry for defect conformal field theories, focusing on codimension one defects like flat boundaries or interfaces. We study surface… Expand

Conformal invariance and the Ising model on a spheroid.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

Conformal mappings between an infinite plane and a spheroid, and one between a semi-infinite plane andA half spheroids are formed, and the magnetic and temperature scaling dimensions are in good agreement with exact results. Expand

Lattice radial quantization: 3D Ising

- Physics
- 2013

Abstract Lattice radial quantization is introduced as a nonperturbative method intended to numerically solve Euclidean conformal field theories that can be realized as fixed points of known… Expand

Conformal Invariance and Surface Critical Behavior

- Physics
- 1984

Abstract Conformal invariance constrains the form of correlation functions near a free surface. In two dimensions, for a wide class of models, it completely determines the correlation functions at… Expand

A Monte Carlo study of surface critical phenomena: The special point

- Physics
- 2011

We study the special point in the phase diagram of a semi-infinite system, where the bulk transition is in the three-dimensional Ising universality class. To this end we perform a finite size scaling… Expand

Finite size scaling study of lattice models in the three-dimensional Ising universality class

- Physics
- 2010

We simulate the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. We perform a finite size scaling study of lattices of a linear size up… Expand