Michael Mann's "hockeystick" says that the LIA did not happen. And in 2007 Phil Jones said "it's important "not to cling to outdated concepts of the past such as the MWP and LIA"
That the "modelling" of the authors below excludes a solar influence as the cause of the LIA need not detain us of course. You can get anything you like out of a model.
GEOPHYSICAL RESEARCH LETTERS, VOL. 39, L02708, 5 PP., 2012
Abrupt onset of the Little Ice Age triggered by volcanism and sustained by sea-ice/ocean feedbacks
by Gifford H. Miller et al.
Northern Hemisphere summer temperatures over the past 8000 years have been paced by the slow decrease in summer insolation resulting from the precession of the equinoxes. However, the causes of superposed century-scale cold summer anomalies, of which the Little Ice Age (LIA) is the most extreme, remain debated, largely because the natural forcings are either weak or, in the case of volcanism, short lived. Here we present precisely dated records of ice-cap growth from Arctic Canada and Iceland showing that LIA summer cold and ice growth began abruptly between 1275 and 1300 AD, followed by a substantial intensification 1430–1455 AD. Intervals of sudden ice growth coincide with two of the most volcanically perturbed half centuries of the past millennium. A transient climate model simulation shows that explosive volcanism produces abrupt summer cooling at these times, and that cold summers can be maintained by sea-ice/ocean feedbacks long after volcanic aerosols are removed. Our results suggest that the onset of the LIA can be linked to an unusual 50-year-long episode with four large sulfur-rich explosive eruptions, each with global sulfate loading >60 Tg. The persistence of cold summers is best explained by consequent sea-ice/ocean feedbacks during a hemispheric summer insolation minimum; large changes in solar irradiance are not required.