Positivity, low twist dominance and CSDR for CFTs

We consider a crossing symmetric dispersion relation (CSDR) for CFT four
point correlation with identical scalar operators, which is manifestly
symmetric under the cross-ratios $u,v$ interchange. This ...

High Energy Physics - Lattice

High Energy Physics - Theory

Optimization and Control

Statistical Mechanics

Strongly Correlated Electrons

Bootstrapping the Ising Model on the Lattice

We study the statistical Ising model of spins on the infinite lattice using a
bootstrap method that combines spin-flip identities with positivity conditions,
including reflection positivity and Griffi ...

A Monte Carlo approach to the conformal bootstrap

We introduce an approach to find approximate numerical solutions of truncated
bootstrap equations for Conformal Field Theories (CFTs) in arbitrary
dimensions. The method is based on a stochastic searc ...

Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model

We construct discrete holomorphic observables in the Ising model at
criticality and show that they have conformally covariant scaling limits (as
mesh of the lattice tends to zero). In the sequel those ...

Topological correlations in three dimensional classical Ising models: an exact solution with a continuous phase transition

We study a three-dimensional (3D) classical Ising model that is exactly
solvable when some coupling constants take certain imaginary values. The
solution combines and generalizes the Onsager-Kaufman s ...

Quantum criticality from Ising model on fractal lattices

We study the quantum Ising model on the Sierpi\'{n}ski triangle, whose
Hausdorff dimension is $\log 3/ \log 2 \approx 1.585$, and demonstrate that it
undergoes second-order phase transition with scali ...

Weizmann Lectures on the Numerical Conformal Bootstrap

These lectures were given at the Weizmann Institute in the spring of 2019.
They are intended to familiarize students with the nuts and bolts of the
numerical bootstrap as efficiently as possible. Afte ...

High Energy Physics - Lattice

High Energy Physics - Phenomenology

High Energy Physics - Theory

Statistical Mechanics

Strongly Correlated Electrons

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications

Conformal field theories have been long known to describe the fascinating
universal physics of scale invariant critical points. They describe continuous
phase transitions in fluids, magnets, and numer ...

High Energy Physics - Lattice

High Energy Physics - Theory

Mathematical Physics

Statistical Mechanics

Strongly Correlated Electrons

Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents

We use the conformal bootstrap to perform a precision study of the operator
spectrum of the critical 3d Ising model. We conjecture that the 3d Ising
spectrum minimizes the central charge c in the spac ...

High Energy Physics - Lattice

High Energy Physics - Theory

Statistical Mechanics

Strongly Correlated Electrons

Carving out OPE space and precise $O(2)$ model critical exponents

We develop new tools for isolating CFTs using the numerical bootstrap. A
"cutting surface" algorithm for scanning OPE coefficients makes it possible to
find islands in high-dimensional spaces. Togethe ...