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The Peierls instability in one-dimensional electron-phonon systems is known to be qualitatively well described by the Mean-Field theory, however the related self-consistent problem so far has only been able to predict a partial suppression of the transition even with proper account of classical lattice fluctuations. Here the Hartree-Fock approximation scheme is extended to the full quantum regime, by mapping the momentum-frequency spectrum of order-parameter fluctuations onto a continuous two-parameter space. For the one-dimensional half-filled Su-Schrieffer-Heeger model the ratio $d=\Omega/2\pi T_c^0$, where $\Omega$ is the characteristic phonon frequency and $2\pi T_c^0$ the lowest finite phonon Matsubara frequency at the mean-field critical point $T_c^0$, provides a natural measure of the adiabaticity of lattice fluctuations. By integrating out finite-frequency phonons, it is found that a variation of $d$ from the classical regime $d=0$ continuously connects $T_c^0$ to a zero-temperature charge-density-wave transition setting up at a finite crossover $d=d_c$. This finite crossover decreases within the range $0\leq d \approx 1$ as the electron-phonon coupling strength increases but remaining small enough for weak-coupling considerations to still hold. Implications of $T_c$ supression on the Ginzburg criterion is discussed, and evidence is given of a possible coherent description of the charge-density-wave problem within the framework of a renormalized Mean-Field theory encompassing several aspects of the transition including its thermodynamics close to the quantum critical point., Comment: 20 pages, 8 figures

We study the role of charge density-wave fluctuations on the temperature dependence of Seebeck coefficient in quasi-one dimensional conductors with a Peierls instability. The description of low-dimensional incommensurate charge density-wave fluctuations as obtained by a generalized Ginzburg-Landau approach for arrays of weakly coupled chains is embodied in the numerical solution of the semi-classical Boltzmann transport equation. The energy and temperature dependence of the scattering time of electrons on fluctuations can then be extracted and its influence on the Seebeck coefficient calculated. The connexion between theory and experiments carried out on molecular conductors is presented and critically discussed., Comment: 9 pages, 5 figures

This work presents and analyzes electrical resistivity data on the organic superconductor (TMTSF)$_2$ClO$_4$ and their anion substituted alloys (TMTSF)$_2$(ClO$_4$)$_{1-x}$(ReO$_4$)$_x$ along the least conducting $c^\star$ axis. Nonmagnetic disorder introduced by finite size domains of anion ordering on non Fermi liquid character of resistivity is investigated near the conditions of quantum criticality. The evolution of the $T$-linear resistivity term with anion disorder shows a limited decrease in contrast with the complete suppression of the critical temperature $T_c$ as expected for unconventional superconductivity beyond a threshold value of $x$. The resulting breakdown of scaling between both quantities is compared to the theoretical predictions of a linearized Boltzmann equation combined to the scaling theory of umklapp scattering in the presence of disorder induced pair-breaking for the carriers., Comment: 13 pages, 8 figures

In the framework of the weak coupling renormalization group technique we examine the possible instabilities of the extended quasi-one-dimensional electron gas model with both intrachain and interchain electron-electron interactions, including the influence of umklapp scattering and the coupling of spins to a magnetic field. In the limit of purely repulsive intrachain interactions, we confirm the passage from singlet d-wave like superconductivity to an inhomogeneous FFLO state under magnetic field. The passage is accompanied by an anomalous increase of the upper critical field that scales with the antinesting distance from the quantum critical point joining superconductivity to antiferromagnetism in the phase diagram, as well as the strength of interactions. Adding weak repulsive interchain interactions promotes the passage from singlet to triplet $f$-wave superconductivity which is expanded under field by the development of a triplet FFLO state with zero angular momentum projection for the Cooper pairs. The connection between theory and experiments on the anomalous upper critical field in the Bechgaard salts is discussed., Comment: 11 pages, 8 figures

We study the influence of inelastic electron-electron scattering on the temperature variation of the Seebeck coefficient in the normal phase of quasi-one-dimensional organic superconductors. The theory is based on the numerical solution of the semi-classical Boltzmann equation for which the collision integral equation is solved with the aid of the electronic umklapp scattering vertex calculated by the renormalization group method. We show that the one-loop renormalization group flow of momentum and temperature dependent umklapp scattering, in the presence of nesting alterations of the Fermi surface, introduce electron-hole asymmetry in the energy dependence of the anisotropic scattering time. This is responsible for the enhancement of the Seebeck coefficient with respect to the band $T$-linear prediction and even its sign reversal around the quantum critical point of the phase diagram, namely where the interplay between antiferromagnetism and superconductivity along with the strength of spin fluctuations are the strongest. Comparison of the results with available data on low dimensional organic superconductors is presented and critically discussed., Comment: 12 pages, 8 figures. Submitted to PRB

We propose a theory of longitudinal resistivity in the normal phase of quasi-one-dimensional organic superconductors near the quantum critical point where antiferromagnetism borders with superconductivity under pressure. The linearized semi-classical Boltzmann equation is solved numerically, fed in by the half-filling electronic umklapp scattering vertex as derived from one-loop renormalization group calculations for the quasi-one-dimensional electron gas model. The momentum and temperature dependence of umklapp scattering has an important impact on the behaviour of longitudinal resistivity in the the normal phase. Resistivity is found to be linear in temperature around the quantum critical point at which spin-density-wave order joins superconductivity along the antinesting axis, to gradually evolve towards the Fermi liquid behaviour in the limit of weak superconductivity. A comparison is made between theory and experiments performed on the (TMTSF)$_2$PF$_6$ member of the Bechgaard salt series under pressure., Comment: 13 pages, 9 figures. Submitted to PRB

We report an investigation of charge, spin and lattice effects in the spin-Peierls state of the organic compound MEM(TCNQ)$_2$. The 16.5 GHz dielectric function along the chain axis shows an enhancement below the spin-Peierls transition temperature near 18 K consistent with the charge coupling to the elastic strain involved in the transition. The velocity of two elastic modes perpendicular to the chain axis presents anomalies at the transition which can be explained with a Landau free energy model including a linear-quadratic coupling energy term between the appropriate elastic strain $e$ and the spin-Peierls magnetic gap $\Delta_q$. The analysis of the dielectric and elastic features aims toward an order parameter with an associated critical exponent $\beta \sim$ 0.36, which is similar to the three-dimensional behavior seen in other spin-Peierls materials. All these effects studied in a magnetic field up to 18 Teslas appear also compatible with a mean-field model of a quasi-one-dimensional spin-Peierls system., Comment: 6 pages, 5 figures

An inductive method is used to follow the magnetic field-dependent susceptibility of the coupled charge density wave (CDW) and spin-Peierls (SP) ordered state behavior in the dual chain organic conductor Perylene$_2$[Pt(mnt)$_2$]. In addition to the coexisting SP-CDW state phase below 8 K and 20 T, the measurements show that a second spin-gapped phase appears above 20 T that coincides with a field-induced insulating phase. The results support a strong coupling of the CDW and SP order parameters even in high magnetic fields, and provide new insight into the nature of the magnetic susceptibility of dual-chain spin and charge systems., Comment: 6 pages, 6 figures

Superconductivity in the Bechgaard salts series of quasi-one-dimensional organic conductors occurs on the verge of spin-density-wave ordering when hydrostatic pressure is applied. The sequence of instabilities is intimately connected to normal state anomalies in various quantities like the temperature dependence of electrical transport and nuclear spin-lattice relaxation rate. We discuss how such a connection takes its origin in the interference between the different pairing mechanisms responsible for antiferromagnetism and superconductivity, a duo that can be comprehended in terms of a weak coupling renormalization group theory. The recent developments along this line of though are presented in relation to experiments., Comment: 11 pages, 6 figures

The phase diagram of the one-dimensional extended Hubbard model at half-filling is investigated by a weak coupling renormalization group method applicable beyond the usual continuum limit for the electron spectrum and coupling constants. We analyze the influence of irrelevant momentum dependent interactions on asymptotic properties of the correlation functions and the nature of dominant phases for the lattice model under study., Comment: 10 pages, 10 figures

We use the weak coupling renormalization group method to examine the interplay between charge-density-wave and s-wave superconducting orders in a quasi-one-dimensional model of electrons interacting with acoustic phonons. The relative stability of both types of order is mapped out at arbitrary nesting deviations and Debye phonon frequency $\omega_D$. We singled out a power law increase of the superconducting $T_c\sim \omega_D^{0.7}$ from a quantum critical point of charge-density-wave order triggered by nesting alterations. The results capture the key features shown by the proximity between the two types of ordering in the phase diagram of the recently discovered Perylene based organic superconductor under pressure. The impact of Coulomb interaction on the relative stability of the competing phases is examined and discussed in connection with the occurrence of s-wave superconductivity in low dimensional charge-density-wave materials., Comment: 6 pages, 5 figures

A linear temperature dependence of the electrical resistivity as T -> 0 is the hallmark of quantum criticality in heavy-fermion metals and the archetypal normal-state property of high-Tc superconductors, yet in both cases it remains unexplained. We report a linear resistivity on the border of spin-density-wave order in the organic superconductor (TMTSF)2X (X = PF6, ClO4), whose strength scales with the superconducting temperature Tc. This scaling, also present in the pnictide superconductors, reveals an intimate connection between linear-T scattering and pairing, shown by renormalization group theory to arise from antiferromagnetic fluctuations, enhanced by the interference of superconducting correlations. Our results suggest that linear resistivity in general may be a consequence of such interference and pairing in overdoped high-Tc cuprates is driven by antiferromagnetic fluctuations, as in organic and pnictide superconductors.

The interdependence of antiferromagnetism and superconductivity in the Bechgaard salts series of organic conductors is examined in the light of the anomalous temperature dependence of the nuclear spin-lattice relaxation rate. We apply the renormalization group approach to the electron gas model to show that the crossover from antiferromagnetism to superconductivity along with the anomalous nuclear relaxation rate of the Bechgaard salts can be well described within a unified microscopic framework. For sizable nesting deviations of the Fermi surface, scaling theory reveals how pairing correlations enhance short-range antiferromagnetic correlations via magnetic Umklapp scattering over a large part of the metallic phase that precedes superconductivity. These enhanced magnetic correlations are responsible for the Curie-Weiss behavior observed in the NMR relaxation rate., Comment: 10 pages, 5 figures

This review covers the study of some basic properties of the phase diagram of quasi-one-dimensional organic superconductors from both experimental and theoretical viewpoints., Comment: 57 pages, 29 figures. This review appeared in the book "Physics of Organic Superconductors and Conductors", edited by A. G. Lebed, Vol. 110, Springer Series in Materials Science (Springer, Heidelberg, 2008). P.357-412

An extension of the renormalization group method that includes the effect of retardation for the interactions of a fermion gas is used to re-examine the quantum and classical properties of Peierls- like states in one dimension. For models of spinless and spin-1/2 fermions interacting with either intra or intermolecular phonons the quantum corrections to the Peierls gap at half-filling are determined at arbitrary phonon frequency. The nature of quantum-classical transitions is clarified in weak coupling., Comment: 15 pages, 8 Figures

The mechanism that drives a metal-insulator transition in an undoped quasi-one-dimensional Mott insulator is examined in the framework of the Hubbard model with two different hoppings t_{perp 1} and t_{perp 2} between nearest-neighbor chains. By applying an N_{perp}-chain renormalization group method at the two-loop level, we show how a metallic state emerges when both t_{perp 1} and t_{perp 2} exceed critical values. In the metallic phase, the quasiparticle weight becomes finite and develops a strong momentum dependence. We discuss the temperature dependence of the resistivity and the impact of our theory in the understanding of recent experiments on half-filled molecular conductors., Comment: 4 pages, 3 figures, published version

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations and both intrachain and interchain repulsive interactions. d-wave superconductivity, which dominates over the spin-density-wave (SDW) phase at large nesting deviations, becomes unstable to the benefit of a triplet $f$-wave phase for a weak repulsive interchain backscattering term $g_1^\perp>0$, despite the persistence of dominant SDW correlations in the normal state. Antiferromagnetism becomes unstable against the formation of a charge-density-wave state when $g_1^\perp$ exceeds some critical value. While these features persist when both Umklapp processes and interchain forward scattering ($g_2^\perp$) are taken into account, the effect of $g_2^\perp$ alone is found to frustrate nearest-neighbor interchain $d$- and $f$-wave pairing and instead favor next-nearest-neighbor interchain singlet or triplet pairing. We argue that the close proximity of SDW and charge-density-wave phases, singlet d-wave and triplet $f$-wave superconducting phases in the theoretical phase diagram provides a possible explanation for recent puzzling experimental findings in the Bechgaard salts, including the coexistence of SDW and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase., Comment: 19 pages, 13 figures

We review the current understanding of superconductivity in the quasi-one-dimensional organic conductors of the Bechgaard and Fabre salt families. We discuss the interplay between superconductivity, antiferromagnetism, and charge-density-wave fluctuations. The connection to recent experimental observations supporting unconventional pairing and the possibility of a triplet-spin order parameter for the superconducting phase is also presented., Comment: (v1) 30 pages, 13 figures; Review article for the 20th anniversary of high-Tc superconductivity, to appear in J. Low Temp. Phys. (v2) 1 Ref. added

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations and both intrachain and interchain repulsive interactions. We find a close proximity of spin-density- and charge-density-wave phases, singlet d-wave and triplet f-wave superconducting phases. There is a striking correspondence between our results and recent puzzling experimental findings in the Bechgaard salts, including the coexistence of spin-density-wave and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase., Comment: 4 pages, 5 eps figures

We study the renormalization of sound attenuation and sound velocity by fluctuation Cooper pairs in layered superconductors. We consider the influence of s- and d-wave symmetry of the fluctuating order parameter, on both longitudinal and transverse phonon modes. We show that both unconventional order parameter symmetry and transverse sound polarization suppress the AL and MT terms, while the DOS contribution is the least affected. The combination of these effects can change the sign of the overall fluctuation corrections above Tc. We also compare the results obtained using the Ginzburg-Landau formalism with a microscopic derivation of the fluctuation corrections to the sound velocity in both s- and d-wave superconductors. These calculations are motivated by ongoing ultrasound measurements in organic superconductors., Comment: 13 pages, 3 figures, 1 table

We consider the temperature dependence of the sound attenuation and sound velocity in layered impure metals due to superconducting fluctuations of the order parameter above the critical temperature. We obtain the dependence on material properties of these fluctuation corrections in the hydrodynamic limit, where the electron mean free path is much smaller than the wavelength of sound and where the electron collision rate is much larger than the sound frequency. For longitudinal sound propagating perpendicular to the layers, the open Fermi surface condition leads to a suppression of the divergent contributions to leading order, in contrast with the case of paraconductivity. The leading temperature dependent corrections, given by the Aslamazov-Larkin, Maki-Thompson and density of states terms, remain finite as T->Tc. Nevertheless, the sensitivity of new ultrasonic experiments on layered organic conductors should make these fluctuations effects measurable., Comment: 13 pages, 6 figures. Accepted for PRB. Added discussion on incoherent interlayer tunneling and other small modifications suggested by referees

We apply the standard Wilson-Kadanoff (WK) momentum-space Renormalization Group (RG) scheme for the g-ology model of one-dimensional fermions. By explicitly carrying out calculations at the two-loop level, we show how the RG flow equations can be derived from the summation of the cascades of contractions generated by the effective action's mode elimination at each infinitesimal step of the WK procedure. The rules for selecting these series of cascades appear naturally as a consequence of the WK scheme ``on-shell'' kinematic constraints and conservation laws. The relation between the present RG approach and the field-theoretic schemes used in earlier related studies is analysed. Generalizations for other models and/or higher dimensions are formulated., Comment: 21 pages, 5 figures

We briefly review the physics of electronic phases in low dimensional conductors. We begin by introducing the properties of the one-dimensional electron gas model using bosonization and renormalization group methods.We then tackle the influence of interchain coupling and go through the different instabilities of the electron system to the formation of higher dimensional states. The connection with observations made in quasi-one-dimensional organic and inorganic conductors is discussed., Comment: LateX, 37 pages, 12 figures, Springer-Verlag macros. Proceedings of the Int. summer school on High Magnetic Fields: Application in Condensed Matter Physics and Spectroscopy, Cargese, May 2001, C. Berthier, L.P. Levy and G. Martinez, Editors, To be pubished by Springer, 2002

We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the scaling ansatz for purely one-dimensional fermion systems and its extension when interchain coupling and dimensionality crossovers are present at finite temperature. Next, we review the application of the renormalization group technique to the one-dimensional electron gas model and clarify some peculiarities of the method at the two-loop level. The influence of interchain coupling is then included and results for the crossover phenomenology and the multiplicity of characteristic energy scales are summarized. The emergence of the Kohn-Luttinger mechanism in quasi-one-dimensional electronic structures is discussed fo both superconducting and density-wave channels., Comment: LateX, 43 pages, 21 figures, Springer Verlag macros. Proc. of International CRM Workshop on Theoretical Methods in Strongly Correlated Fermions Systems, May 1999, Montreal, to be published by Springer (2002)

We use the Density-Matrix Renormalization Group to study the single-particle and two-particle correlation functions of spinless fermions in the ground state of a quarter-filled ladder. This ladder consists of two chains having an in-chain extended Coulomb interaction reaching to third neighbor and coupled by inter-chain hopping. Within our short numerical coherence lengths, typically reaching ten to twenty sites, we find a strong renormalization of the interchain hopping and the existence of a dimensional crossover at smaller interactions. We also find power exponents for single-particle hopping and interchain polarization consistent with the single chain. The total charge correlation function has a larger power exponent and shows signs of a crossover from incoherent fermion hopping to coherent particle-hole pair motion between chains. There are no significant excitation energies., Comment: RevTex 4 file, 10 pages, 10 eps figures

We use the momentum space renormalization group to study the influence of phonons and the Coulomb interaction on the superconducting response function of armchair single-walled nanotubes. We do not find superconductivity in undoped single nanotubes. When doped, superconducting fluctuations can develop because of the phonons but remain small and are easily destroyed by the Coulomb interaction. The origin of superconductivity in ropes of nanotobes is most likely an intertube effect. Projections to zig-zag nanotubes indicate a more favorable disposition to superconducting fluctuations., Comment: RevTex file, 3 eps Figures

(63)Cu-NMR measurements have been performed on two-leg hole-doped spin ladders Sr_{14-x}Ca_{x}Cu_{24}O_{41} single crystals (0-x-12) at several pressures up to the pressure domain where the stabilization of a superconducting ground state can be achieved. The data reveal marked decrease of the spin gap derived from Knight shift measurements upon Ca substitution and also under pressure and confirm the onset of low lying spin excitations around P_{c} as previously reported. The spin gap in Sr_{2}Ca_{12}Cu_{24}O_{41} is strongly reduced above 20 kbar. However, the data of an experiment performed at P=36 kbar where superconductivity has been detected at 6.7K by an inductive technique have shown that a significant amount of spin excitations remains gapped at 80K when superconductivity sets in. The standard relaxation model with two and three-magnon modes explains fairly well the activated relaxation data in the intermediate temperature regime corresponding to gapped spin excitations using the spin gap data derived from Knight shift experiments.The data of Gaussian relaxation rates of heavily doped samples support the limitation of the coherence lenght at low temperature by the average distance between doped holes. We discuss the interplay between superconductivity and the spin gap and suggest that these new results support the exciting prospect of superconductivity induced by the interladder tunnelling of preformed pairs as long as the pressure remains lower than the pressure corresponding to the maximum of the superconducting critical temperature., Comment: 15 pages Latex, 13 figures. to be published in Eur.Phys.Jour.B,2002

The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a continuous crossover from a spin-density-wave state to unconventional superconductivity when deviations from perfect nesting of the Fermi surface exceed a critical value. Singlet pairing between electrons on neighboring stacks is found to be the most favorable symmetry for superconductivity. The consequences of non uniform spin-density-wave pairing on the structure of phase diagram within the crossover region is also discussed., Comment: 10 pages RevTex,4 Figures, submitted to EPJB

This paper is written as a brief introduction for beginning graduate students. The picture of electron waves moving in a cristalline potential and interacting weakly with each other and with cristalline vibrations suffices to explain the properties of technologically important materials such as semiconductors and also simple metals that become superconductors. In magnetic materials, the relevant picture is that of electrons that are completely localized, spin being left as the only relevant degree of freedom. A number of recently discovered materials with unusual properties do not fit in any of these two limiting cases. These challenging materials are generally very anisotropic, either quasi one-dimensional or quasi two-dimensional, and in addition their electrons interact strongly but not enough to be completely localized. High temperature superconductors and certain organic conductors fall in the latter category. This paper discusses how the effect of low dimension leads to new paradigms in the one-dimensional case (Luttinger liquids, spin-charge separation), and indicates some of the attempts that are being undertaken to develop, concurrently, new methodology and new concepts for the quasi-two-dimensional case, especially relevant to high-temperature superconductors., Comment: 9 pages, RevTeX. A shorter version of this paper has been submitted to appear in a special issue of "Physics in Canada" devoted to superconductivity

In this brief account, we shall review the different mechanisms giving rise to itinerant and localized antiferromagnetism in quasi-one-dimensional organic conductors: the Bechgaard salts and their sulfur analogs. We will then focus on the problem of spin correlations and their impact on the pairing mechanism for organic superconductivity., Comment: 7 pages, 5 figures, RevTex

The phase diagram of the layered organic superconductor $\kappa$-(ET)$_{2}$Cu[N(CN)$_{2}$]Cl has been accurately measured from a combination of $^{1}$H NMR and AC susceptibility techniques under helium gas pressure. The domains of stability of antiferromagnetic and superconducting long-range orders in the pressure {\it vs} temperature plane have been determined. Both phases overlap through a first-order boundary that separates two regions of inhomogeneous phase coexistence. The boundary curve is found to merge with another first order line related to the metal-insulator transition in the paramagnetic region. This transition is found to evolve into a crossover regime above a critical point at higher temperature. The whole phase diagram features a point-like region where metallic, insulating, antiferromagnetic and non s-wave superconducting phases all meet., Comment: 4 pages, 6 figures, Revtex

We reexamine the putative Peierls transition in a (5,5) metallic nanotube. We show that the conduction electrons at the Fermi level do not couple to the longitudinal acoustic phonon but rather to a folded-in graphene zone edge phonon having the proper Kekule modulation symmetry. The calculation for the mean-field transition temperature gives 15 K, a value comparable to previous estimates. We discuss the significance of this transition temperature., Comment: 4 pages, 2 figures, LaTex, submitted to Phys. Rev. B

We review the properties of quasi-one-dimensional organic superconductors: the Bechgaard salts and their sulfur analogs in their normal phase precursor tolong-range order. We go through the main observations made in the normal state of these systems at low magnetic field and tackle the issue of their description under the angles of the Fermi and Luttinger liquid pictures., Comment: Latex, 26 pages, 27 eps figures, ICSM.sty. Review paper to be pubished in Proc. of Int. Conf. of Science and Technology of Synthetic Metals (ICSM'98), Elsevier 1999

The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reaveals that the Luttinger liquid spin susceptibility $\chi (T) $ approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given., Comment: 21 pages, latex including 5 eps figures

Transport and 63^Cu-NMR, Knight shift and T_1, measurements performed on the two-leg spin ladders of Sr_2Ca_{12}Cu_{24}O_{41} single crystals show a collapse of the gap in ladder spin excitations when superconductivity is stabilised under a pressure of 29 kbar. These results support the prediction made with exact diagonalisation techniques in two-leg isotropic t-J ladders of a transition between a low-doping spin gap phase and a gapless 1-D Tomonaga-Luttinger regime., Comment: 6 pages, latex, 4 postscript figures included, submitted to Science

It is shown that the Luttinger liquid is unstable to arbitrarily small transverse hopping. It becomes either a Fermi liquid or exhibits long-range order at zero temperature. The crossover temperatures below which either transverse coherent band motion or long-range order start to develop can be finite even when spin and charge velocities differ. Explicit scaling relations for the one-particle and two-particle crossover temperatures are derived in terms of transverse hopping amplitude, spin and charge velocities as well as anomalous exponents. The special case of infinite-range transverse hopping can be treated exactly and yields a Fermi liquid down to zero temperature, unless the anomalous exponent $\theta $ is larger than unity., Comment: J1K 2R1 REVTEX 3.0, one figure available on request, Report # CRPS-94-10