Publications of Giuseppe Benfatto
a) Mathematical Physics
1. DLR measures for one dimensional harmonic systems - Zeit. Wahrsch. 41, 305-312, 1978 - with
2. The local Von Neumann algebras for the zero mass scalar free field and
the free electromagnetic field
- J. Math. Physics
19, 653-660, 1978 - with F. Nicolò.
3. Introduzione alla teoria delle Algebre di Von Neumann e Teorema di Tomita-Takesaki (notes about a course given by S. Doplicher) - Quaderni del CNR, 1977 - with C. D'Antoni, F. Nicolò and G.C. Rossi.
4.
Some probabilistic techniques in field theory - Comm. Math.
Phys. 59, 143-166, 1978 - with
M. Cassandro,
5. Elliptic equations and gaussian processes
- J. Funct. Anal. 36, 343-400, 1980 - with
6.
Ultraviolet stability in the euclidean scalar
field theories - Comm. Math. Phys.
71, 95-130, 1980 - with M. Cassandro,
7. Superstability estimates for anharmonic systems - J. Stat. Phys. 22, 349-362,
1980 - with C. Marchioro,
8. Gaussian processes and constructive scalar field theory – Random fields, Vol. I, II (Esztergom, 1979), 109-144, Colloq. Math.
Soc. János Bolyai, 27, North-Holland,
1981 - with F. Nicolò.
9. The renormalization group in the euclidean
scalar renormalizable field theories - Mathematical problems in theoretical
physics (Proc. ``Intern. Conf. Math. Phys.'', Lausanne, 1979), 211-216, Lecture
Notes in Physics 116,
Springer-Verlag, 1980.
10. On the massive sine-Gordon equation in the first few regions of
collapse -
Comm. Math. Phys. 83, 387-410, 1982 - with
11. A diffusion process associated to the Prandtl
equation -
J. Funct. Anal. 52, 330-343, 1983 - with M.
Pulvirenti.
12. Exact decay of correlations for infinite range continuous systems
- Helv Phys. Acta 57, 63-85,
1984 - with Ch. Gruber and Ph.A. Martin.
13. On the susceptibility and clustering properties of unbounded spins - J. Stat. Phys. 37,
237-256, 1984 - with Ch. Gruber.
14. Generation of vorticity near the boundary in
planar Navier-Stokes flows - Comm. Math. Phys. 96,
59-95, 1984 - with M. Pulvirenti.
15. Planar Navier-Stokes flow for singular
initial data - J. Nonlinear Anal. 9, 533-545, 1985 - with R. Esposito and M.
Pulvirenti.
16. Vortex methods in planar fluidodynamics
- Applications of mathematics in technology
(Rome, 1984), 141-164, Teubner, Stuttgart, 1984 -
with C. Marchioro and M. Pulvirenti.
17. An iterated Mayer expansion for the Yukawa gas - J. Stat. Phys. 41, 671-684,
1985.
18. Convergence of the Chorin-Marsden algorithm
in the half-plane - Comm. Math. Phys. 106, 427-458, 1986 - with M. Pulvirenti.
19. The dipole phase in the two-dimensional hierarchical Coulomb gas:
analyticity and correlations decay - Comm. Math. Phys. 106, 277-288, 1986 -
with
20. On the invariant measures for the two-dimensional Euler flow - J. Stat. Phys. 46,
729-742, 1987 - with P. Picco and M. Pulvirenti.
21. On the analyticity of the pressure in the hierarchical dipole gas
- J. Stat. Phys. 55,
739-744, 1989 - with
22. Perturbation theory of the Fermi surface in a quantum liquid. A general
quasi particle formalism and one dimensional systems - J. Stat. Phys. 59, 541-664,
1990 - with G. Gallavotti.
23. Renormalization
group approach to the theory of the Fermi surface - Phys. Rev. B 42,
9967-9972, 1990 - with G. Gallavotti.
24. Renormalization
group and the Fermi surface in the Luttinger model - Phys. Rev. B 45, 5468-5480, 1992 - with G. Gallavotti and V. Mastropietro.
25. The one-dimensional spinless Fermi gas and the Luttinger model - Probabilistic Methods in Math. Physics (Siena, 6-11 maggio 1991), 70-82, World Scientific, 1992.
26. Nontrivial fixed points
and screening in the hierarchical two-dimensional Coulomb gas - J. Stat. Phys. 67,
957-980, 1992 - with J. Renn.
27. Beta function and Schwinger functions for a many fermions system in one
dimension. Anomaly of the Fermi surface. - Commun.
Math. Phys. 160, 93-171, 1994 - with
28. Some numerical results on the block spin transformation for the 2D Ising model at the critical point. - J. Stat. Phys. 78,
731-757, 1995 - with E. Marinari and E. Olivieri.
29. Renormalization group approach to zero temperature Bose condensation
- Constructive results in Field Theory,
Statistical Mechanics and Condensed Matter Physics (Palaiseau,
July 25-27, 1994), 219-247, Lecture Notes in Physics 446, Springer, 1995.
30. Disorder in the 1D spinless Holstein model
- Helvetica Physica Acta 68, 312-327,
1995 - with
31. Renormalization group - Physics notes 1, Princeton University Press,
1995 - with G. Gallavotti.
32. Renormalization group approach to zero temperature Bose condensation
- Math. Phys. Electron. J. 2, paper 3, 9pp. (electronic), 1996.
33. Electrons in a lattice with an incommensurate potential - J. Stat. Physics 89,
655-708, 1997. - with
34. Peierls
instability for the Holstein model with rational density - J. Stat. Physics 92,
1071-1113, 1998. - with
35. Peierls
instability for the Holstein model - Mathematical
Results in Statistical Mechanics" (Marseilles, July 27-31, 1998),
149-162, World Scientific, 1999.
36. An approximate KAM-Renormalization-Group scheme for Hamiltonian systems
- J. Stat. Physics
94, 241-251, 1999.- with C. Chandre and H.R.
Jauslin.
37. Approximate renormalization-group transformation for Hamiltonian
systems with three degrees of freedom - Phys. Rev. E60, 5412-5421, 1999.- with
38. Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
- Physica D 154, 159-170, 2001.- with C. Chandre, H. Jauslin, J. Laskar.
39. Renormalization Group, hidden symmetries and approximate Ward identities
in the XYZ model - Rev. Math. Phys. 13, 1323-1435, 2001- with V. Mastropietro.
40. On the density-density critical indices in interacting Fermi systems
- Comm. Math.
Phys. 231, 97-134, 2002. - with V. Mastropietro.
41. Low temperature
analysis of two dimensional Fermi systems with symmetric Fermi surface – Annales
Henri Poincaré
4, 137-193, 2003 – with
42. Ward identities and
vanishing of the beta function for $d=1$
interacting Fermi systems – J. Stat. Phys. 115, 143-184, 2004 – with V. Mastropietro.
43. Ward identities and Chiral anomaly in the Luttinger
liquid – Comm.
Math. Phys. 258, 609-655, 2005 - with V. Mastropietro.
44. Limit theorems for
statistics of combinatorial partitions with applications to mean field Bose gas – J. Math. Phys. 46, 03303,
2005 - with M. Cassandro, I. Merola
and
45. Rigorous analysis of
the Tomonaga model by means of Ward identities and
the renormalization group – J. Stat. Mech. L04001, 2005 – with V. Mastropietro.
46. Fermi liquid behavior in the 2D Hubbard model at low temperatures – Annales
Henri Poincaré 7,
809-898, 2006 – with
47. Functional integral
construction of the massive Thirring model:
verification of the axioms and massless limit – Comm. Math. Phys.
273, 67-118, 2007 – with P. Falco and V. Mastropietro.
48. Massless
Sine-Gordon and Massive Thirring Models: proof of the
Coleman's equivalence – Comm. Math.
Phys. 285, 713-762, 2009 – with P.
Falco and V. Mastropietro.
49. On the ultraviolet
problem for the 2D weakly interacting Fermi gas – Annales
Henri Poincaré 10,
1-17, 2009.
50. Rigorous construction of Luttinger liquids through Ward Identities - New Trends in Mathematical Physics, Selected contributions of the XVth
International Congress on Mathematical Physics, Sidoravicius V. Ed., Springer,
2009.
51. Extended scaling
relations for planar lattice models – Comm. Math. Phys. 292, 569-605, 2009 – with P. Falco and V. Mastropietro.
52. Universality
relations in non-solvable quantum spin chains – J. Stat. Phys., 138, 1084 – 1108, 2010 – with V. Mastropietro.
53. Universality relations for nonsolvable statistical models – Phys.
Rev. Lett., 104, 075701, 2010 – with P. Falco and V. Mastropietro.
54. Drude weight in non solvable quantum spin chains – J. Stat. Phys., 143(2), 251-260, 2011 - with V. Mastropietro.
55. Universal Luttinger
Liquid Relations in the 1D Hubbard Model – arXiv:1106.0356v1
[math-ph] 2 Jun 2011 - with P. Falco and V. Mastropietro.
56. Universality of one-dimensional Fermi
systems, I. Response functions and critical exponents - Comm. Math. Phys., march 2014, DOI: 10.1007/S00220-014-2008-y - with P. Falco and V. Mastropietro.
57. Universality of one-dimensional Fermi
systems, II. The Luttinger liquid structure - Comm. Math. Phys., march 2014, DOI: 10.1007/S00220-014-2009-x - with P. Falco and V. Mastropietro.
58. Kondo Effect in a Fermionic Hierarchical Model - J. Stat. Phys., 138(5), 1203-1230, 2015 – with G.
Gallavotti and J. Jauslin.
b) Theoretical Physics