should be contrasted with the one observed below φ$_{c}$ , where a large but finite correlation length has been identified, which is governed by the approach to point J. 51 Upon increasing the strain-rate we have shown that the correlation length starts to decrease out- side the finite-size scaling regime (Fig. 10). Olsson and Teitel 26 infer from their flow simulations that shear-stress should be viewed as a “relevant pertur- bation” to point J, such that a different fixed-point and indeed different physics is relevant for the flow behaviour at finite stress. Our findings support this picture for the dynamical correlations, which ap- pear to behave similarly to those observed in mod- els of elasto-plastic flow 13,14,52 or in low temper- ature glasses: 10,15 correlations increase upon low- ering the strain-rate and saturate at a system-size dependent value in the quasistatic regime. The flow behaviour in the vicinity of point J is therefore influenced by a complex combination of two critical behaviour. Large stress fluctuations (relative to the yield stress), or geometrical changes (number of neighbours) reflect the enhanced sen- sitivity of the material to small changes in exter- nal conditions at point J, and are specific proper- ties of the energy landscape at this point. On the other hand, dynamical correlations above point J are dominated by the system size, and build up progressively as the strain rate is decreased, as in any elasto-plastic system, and are not particularly sensitive to the proximity of point J. Acknowledgments The authors acknowledge fruitful discussions with Ludovic Berthier, Lyd´ eric Bocquet, Erwin Frey; Craig Maloney and Michel Tsamados, as well as thank the von-Humboldt Feodor-Lynen, the Marie-Curie Eurosim and the ANR Syscom program for financial support. References [1] A. J. Liu and S. R. Nagel, Nature , 1998, 396 , 21. [2] M. Dennin, J. Phys. Cond. Matt. , 2008, 20 , 283103. [3] A. S. Argon, Acta Metall. , 1979, 27 , 47. [4] A. S. Argon and L. T. Shi, Acta Metall. , 1983, 31 , 499. [5] M. L. Falk and J. S. Langer, Phys. Rev. E , 1998, 57 , 7192. [6] E. Bouchbinder, J. S. Langer and I. Procaccia, Phys. Rev. E , 2007, 75 , 036107. [7] D. L. Malandro and D. J. Lacks, J. Chem. Phys. , 1999, 110 , 4593. [9] A. Lemaitre and C. Carol, Phys. Rev. E , 2007, 76 , 036104. [8] C. E. Maloney and A. Lemaˆıtre, Phys. Rev. E , 2006, 74 , 016118. [10] A. Tanguy, F. Leonforte and L.-L. Barrat, Eur. Phys. J. E , 2006, 20 , 355. [11] M. Tsamados, A. Tanguy, F. L´ eonforte and J.-L. Barrat, Eur. Phys. J. E , 2008, 26 , 283. [12] M. Tsamados, A. Tanguy, C. Goldenberg and J.-L. Barrat, Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) , 2009, 80 , 026112. [13] L. Bocquet, A. Colin and A. Ajdari, Physical Review Letters , 2009, 103 , 036001. [14] G. Picard, A. Ajdari, F. Lequeux and L. Boc- quet, Phys. Rev. E , 2005, 71 , 010501(R). [15] A. Lemaˆıtre and C. Caroli, Physical Review Letters , 2009, 103 , 065501. [16] C. S. O’Hern, L. E. Silbert, A. J. Liu and S. R. Nagel, Phys. Rev. E , 2003, 68 , 11306. [17] T. S. Majmudar, M. Sperl, S. Luding and R. P. Behringer, Phys. Rev. Lett. , 2007, 98 , 058001. [18] J. C. Maxwell, Philos. Mag. , 1864, 27 , 27. [19] C. R. Calladine, Int. J. Solids Struct. , 1978, 14 , 161. [20] D. J. Durian, Phys. Rev. Lett. , 1995, 75 , 4780– 4783. [21] M. Wyart, Ann. Phys. Fr. , 2005, 30 , 1. [22] W. G. Ellenbroek, E. Somfai, M. van Hecke and W. van Saarloos, Phys. Rev. Lett. , 2006, 97 , 258001. 11