Correction for Franz et al., Quantitative field theory of the glass transition

PHYSICS Correction for “Quantitative field theory of the glass transition,” by Silvio Franz, Hugo Jacquin, Giorgio Parisi, Pierfrancesco Urbani, and Francesco Zamponi, which appeared in issue 46, November 13, 2012, of Proc Natl Acad Sci USA (109:18725–18730; first published October 29, 2012; 10.1073/pnas.1216578109).

On page 18727, right column, Eq.12 should instead appear as

On page 18728, right column, Eq. 21 should instead appear as

The authors note that Tables 1 and 2 appeared incorrectly. The corrected tables appear below.

Table 1.

Numerical values of the coefficients of the effective action and the physical quantities from the HNC approximation

System	T						σ	μ	λ			Gi
SS-6	1	6.691	3.88	1.35	-0.000925	0.000110	0.000195	0.000525	0.348	0.601	224	0.0267
SS-9	1	2.912	0.0000772	0.0000272	-0.00539	0.000633	0.00163	0.00543	0.353	0.548	34.3	0.0125
SS-12	1	2.057	0.000275	0.0000973	-0.0116	0.00132	0.00378	0.0152	0.354	0.498	14.2	0.0118
LJ	0.7	1.407	0.00106	0.000376	-0.0258	0.00290	0.00989	0.0414	0.355	0.489	6.00	0.00833
HarmS		1.336	0.00129	0.000465	-0.0336	0.00343	0.00772	0.0779	0.359	0.315	2.82	0.0434
HarmS		1.196	0.00165	0.000622	-0.0403	0.00386	0.00819	0.109	0.378	0.274	1.69	0.0632
HarmS		1.170	0.00174	0.000663	-0.0416	0.00395	0.00845	0.109	0.382	0.278	1.66	0.0635
HS	0	1.169	0.00174	0.000664	-0.0418	0.00397	0.00847	0.108	0.381	0.280	1.67	0.0639

For each potential, lengths are given in units of and energies in units of ϵ, with . Data at fixed temperature, using density as a control parameter with .

Table 2.

Same as Table 1, but here the data are at fixed density, using temperature as a control parameter with

System	ρ						σ	μ	λ			Gi
LJ	1.2	0.336	0.00186	0.000663	-0.0361	0.00403	0.0147	0.0572	0.356	0.507	4.56	0.00730
LJ	1.27	0.438	0.00153	0.000541	-0.0321	0.00370	0.0128	0.0447	0.353	0.536	5.74	0.00771
LJ	1.4	0.684	0.00108	0.000383	-0.0260	0.00293	0.0100	0.0292	0.355	0.586	8.52	0.00825
WCA	1.2	0.325	0.00195	0.000686	-0.0389	0.00426	0.0133	0.0607	0.351	0.467	4.37	0.0134
WCA	1.4	0.692	0.00111	0.000388	-0.0270	0.00301	0.00966	0.0291	0.350	0.576	8.67	0.0106