## 24 Citations

### Wilson–Polchinski exact renormalization group equation for O (N) systems: leading and next-to-leading orders in the derivative expansion

- Mathematics
- 2005

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this…

### Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

- Physics
- 2007

We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice.…

### Universality and the renormalisation group

- Physics
- 2005

Several functional renormalisation group (RG) equations including Polchinski flows and Exact RG flows are compared from a conceptual point of view and in given truncations. Similarities and…

### Reparameterization invariance and RG equations: extension of the local potential approximation

- Mathematics, Physics
- 2009

Equations related to the Polchinski version of the exact renormalization group (RG) equations for scalar fields which extend the local potential approximation to first order in a derivative…

### Integrability properties of renormalization group flow

- Mathematics
- 2017

We consider the Polchinski RG equation for a theory of matrix scalar fields interacting with single trace operators and show that it can be written in a Hamiltonian form for a specific choice of the…

### Optimization of field-dependent nonperturbative renormalization group flows

- Physics
- 2005

We investigate the influence of the momentum cutoff function on the field-dependent nonperturbative renormalization group flows for the three-dimensional Ising model, up to the second order of the…

### The fate of non-polynomial interactions in scalar field theory

- Physics
- 2018

We present an exact RG (renormalization group) analysis of O(N)-invariant scalar field theory about the Gaussian fixed point. We prove a series of statements that taken together show that the…

### Equivalence of local potential approximations

- Mathematics
- 2005

In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents…

## References

SHOWING 1-10 OF 53 REFERENCES

### The renormalization group: Critical phenomena and the Kondo problem

- Physics
- 1975

This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in…

### Optimization of the derivative expansion in the nonperturbative renormalization group

- Physics, Mathematics
- 2003

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the…

### Fast-convergent resummation algorithm and critical exponents of φ4-theory in three dimensions

- Mathematics
- 2001

We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant gB for which we possess a finite number L of expansion coefficients…