There is, naturally, more than one access point to Ireland's Two Door Cinema Club. To some they're the grassroots, hype-free success rejuvenating guitar music from the wafty jangle up. To others, they're the ubiquitous advert band who have made math-pop – a style characterised by fiddly high-pitched guitar work resembling the Smiths trapped down a mine shaft, panicking – radio-friendly by straddling the gaping divide between Foals and Keane.

Both are equally valid ways in and, combined, they've made TDCC a genuine phenomenon. Their second album, Beacon, the virulent word-of-mouth hit of two festival seasons, is currently battling the Vaccines for No 1. They could sell out the Empire for a week, but instead celebrate Beacon's release with one "thank you" show for their famously frenetic fans, a throwback to their breakthrough gig here a year ago that, says baby-faced singer Alex Trimble, "feels like we're reliving a really weird dream".

The cause of all this Cinemania swiftly becomes evident. TDCC deliver a relentless 70-minute rush of taut euphoria, a runaway train of a gig. Beacon is far more sophisticated and worldly than 2010's debut, Tourist History, replacing the youthful optimism of This Is the Life and the calypso tongue-twister Something Good Can Work with songs about homesickness, drugs, ABH and dumping perfectly nice girls. But it doesn't drop any pace, only adding meat and muscle to TDCC's populist melding of Friendly Fires, Foals and Vampire Weekend. Once you could have called their hits interchangeable, now they're gaining character.

Next Year is a desert storm, bassist Kevin Baird strips to a black weightlifter's vest to thunk weighty funk on to Wake Up, and Handshake resembles a disco Death Cab for Cutie, Trimble's airy vocals bringing to mind the flawed-crystal whine of Death Cab's Ben Gibbard. TDCC are fast becoming something good, working superbly.

What have you been to see lately? Tell us about it on Twitter using #GdnReview